Write each expression in terms of sine and​ cosine, and then simplify so that no quotients appear in the final expression and all functions are of x only.
[tex]\frac{csc^2 (-x)-1}{1-cos^2 (-x)}[/tex]

Answers

Answer 1

[tex]\stackrel{\textit{reciprocal ident.}}{csc(\theta)=\cfrac{1}{sin(\theta)}} ~\hfill \stackrel{\textit{symmetry ident.}}{sin(-\theta )=-sin(\theta)}~\hfill \begin{array}{llll} \stackrel{\textit{pythagorean ident.}}{sin^2(\theta)+cos^2(\theta)=1}\\ sin^2(\theta)=1-cos^2(\theta)\\ cos^2(\theta)=1-sin^2(\theta) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\cfrac{csc^2(-x)-1}{1-cos^2(-x)}\implies \cfrac{~~\frac{1}{sin^2(-x)}-1~~}{sin^2(-x)}\implies \cfrac{~~ \frac{1-sin^2(-x)}{sin^2(-x)}~~}{\frac{sin^2(-x)}{1}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{keeping in mind that}~\hfill }{sin^2(-x)\implies [sin(-x)]^2\implies [-sin(x)]^2\implies [sin(x)]^2\implies sin^2(x)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{~~ \frac{1-sin^2(x)}{sin^2(x)}~~}{\frac{sin^2(x)}{1}}\implies \cfrac{1-sin^2(x)}{sin^2(x)}\cdot \cfrac{1}{sin^2(x)}\implies \cfrac{cos^2(x)}{sin^2(x)}\cdot \cfrac{1}{sin^2(x)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill cot^2(x)csc^2(x)~\hfill[/tex]


Related Questions

1. Divide
(7x2 - 13x+4) - (x-1
)

Answers

Answer:7 x 2 − 14 x + 5

Step-by-step explanation:

1 In general, given a{x}^{2}+bx+cax  

2

+bx+c, the factored form is:

a(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a})(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a})

a(x−  

2a

−b+  

b  

2

−4ac

 

)(x−  

2a

−b−  

b  

2

−4ac

 

)

2 In this case, a=7a=7, b=-14b=−14 and c=5c=5.

7(x-\frac{14+\sqrt{{(-14)}^{2}-4\times 7\times 5}}{2\times 7})(x-\frac{14-\sqrt{{(-14)}^{2}-4\times 7\times 5}}{2\times 7})

7(x−  

2×7

14+  

(−14)  

2

−4×7×5

 

)(x−  

2×7

14−  

(−14)  

2

−4×7×5

 

)

3 Simplify.

7(x-\frac{14+2\sqrt{14}}{14})(x-\frac{14-2\sqrt{14}}{14})

7(x−  

14

14+2  

14

 

)(x−  

14

14−2  

14

 

)

4 Factor out the common term 22.

7(x-\frac{2(7+\sqrt{14})}{14})(x-\frac{14-2\sqrt{14}}{14})

7(x−  

14

2(7+  

14

)

)(x−  

14

14−2  

14

 

)

5 Simplify  \frac{2(7+\sqrt{14})}{14}  

14

2(7+  

14

)

  to  \frac{7+\sqrt{14}}{7}  

7

7+  

14

 

.

7(x-\frac{7+\sqrt{14}}{7})(x-\frac{14-2\sqrt{14}}{14})

7(x−  

7

7+  

14

 

)(x−  

14

14−2  

14

 

)

6 Simplify  \frac{7+\sqrt{14}}{7}  

7

7+  

14

 

  to  1+\frac{\sqrt{14}}{7}1+  

7

14

 

.

7(x-(1+\frac{\sqrt{14}}{7}))(x-\frac{14-2\sqrt{14}}{14})

7(x−(1+  

7

14

 

))(x−  

14

14−2  

14

 

)

7 Remove parentheses.

7(x-1-\frac{\sqrt{14}}{7})(x-\frac{14-2\sqrt{14}}{14})

7(x−1−  

7

14

 

)(x−  

14

14−2  

14

 

)

8 Factor out the common term 22.

7(x-1-\frac{\sqrt{14}}{7})(x-\frac{2(7-\sqrt{14})}{14})

7(x−1−  

7

14

 

)(x−  

14

2(7−  

14

)

)

9 Simplify  \frac{2(7-\sqrt{14})}{14}  

14

2(7−  

14

)

  to  \frac{7-\sqrt{14}}{7}  

7

7−  

14

 

.

7(x-1-\frac{\sqrt{14}}{7})(x-\frac{7-\sqrt{14}}{7})

7(x−1−  

7

14

 

)(x−  

7

7−  

14

 

)

10 Simplify  \frac{7-\sqrt{14}}{7}  

7 7−  14  to  1-\frac{\sqrt{14}}{7}1−  7 14

7(x-1-\frac{\sqrt{14}}{7})(x-(1-\frac{\sqrt{14}}{7}))

7(x−1−  7 /14 )(x−(1−  7 14 )) 11 Remove parentheses.

7(x-1-\frac{\sqrt{14}}{7})(x-1+\frac{\sqrt{14}}{7})

7(x−1−  7/ 14 .7(x−1+ 7 14 )

Solve the system of equations.
\begin{aligned} & -4x+3y = -2 \\\\ & y=x-1 \end{aligned}


−4x+3y=−2
y=x−1

Answers

Answer:

x = -1 ; y=0

Step-by-step explanation:

We plug in the y, from the second equation, in the first one. By doing so we obtain:

-4x +3(x-1) = -2

-4x + 3x - 3 =-2

-x = 1

x= -1

Now we take this value and plug it in the second equation:

y = 1-1 = 0

Solution:

(-1,0)

-4x+3(x-1)=-2
-4x+3x-3=-2
-4x+3x=-2+3
-x=1
x=-1

y=-1-1
y=-2

(x,y)
(-1, -2)

PLSSS help now!!!!!! Will mark Brainlyest !!!

Answers

the answer is (-7,-4) is your answer

Hope this helps :)

Answer:

  (7, -4)

Step-by-step explanation:

Rotation 180° causes both coordinates to change sign. It is the same as reflection across the origin, or  reflection across both the x- and y-axes.

The image point is (7, -4).

Write down three integers, all less than 25, whose
• range is 10, and
• mean is 13.
The three integers are

Answers

Answer: 9 11 19

Step-by-step explanation

9 11 19

Answer:

18 and 8

Step-by-step explanation:

Range= 18-8

Mean=(18+8)/2=13

PLEASE HELP DUE RIGHT NOW!!!

Answers

Answer:

linear

Step-by-step explanation:

50 POINTS FOR EACH PERSON PLSSSSS HELP!!!!!

∫[tex]x^{\frac{3}{2} }[/tex]㏑(x) dx

Answers

Answer:

Look at images below ^^

Step-by-step explanation:

I'm not sure if they are correct, since I'm not there yet. But I hope it's correct.

( I will give brainliest! ) What is the simplified expression of

4x + 2(3x + 7) - 7x?

Answers

Answer:

[tex]3x + 14[/tex]

Step-by-step explanation:

Step 1:  Distribute

[tex]4x + 2(3x + 7) - 7x[/tex]

[tex]4x + (2 * 3x) + (2 * 7) - 7x[/tex]

[tex]4x + 6x + 14 - 7x[/tex]

Step 2:  Combine like terms

[tex]4x + 6x + 14 - 7x[/tex]

[tex](4x + 6x - 7x) + 14[/tex]

[tex]3x + 14[/tex]

Answer:  [tex]3x + 14[/tex]

Given f(x)=9-2x, find f(10).

A.-11
B.11
C.29
D.-29

Answers

Answer:

the answer is A

Step-by-step explanation:

9-2(10)         9-20

The given function is a linear function that decreases as the value of the

input x increases.

The value of f(10), given f(x) = 9 - 2·x is option A. -11

Reasons:

The given function is f(x) = 9 - 2·x

The output of the function is the value of f(x) for a given input x of the function.

The input value, x is substituted into the function to obtain the output value, f(x).

Given that the input, x = 10

We have;

f(10) = 9 - 2×10 = -11

Therefore, the correct option for f(10) is A. -11

Learn more about functions here:

https://brainly.com/question/10781304

Which inequality does the graph represent?

Answers

Answer:

x < -y + 1

Step-by-step explanation:

MCQS:
Solve for X: X-3 = 27/64

A. 42
B. 43
C. 34
D. 14

Answers

Answer:

219/64

Step-by-step explanation:

x - 3 = 27/64

64(x - 3) = 27

64x - 192 = 27

64x = 27 + 192

64x = 219

x = 219/64

Answer:

[tex]x = 3.4218[/tex]

Step-by-step explanation:

[tex]x -3=\frac{27}{64}[/tex]

[tex]64(x-3)=27[/tex]

[tex]64x-192=27[/tex]

[tex]64x=27+192[/tex]

[tex]64x=219[/tex]

[tex]\frac{64x}{64} =\frac{219}{64}[/tex]

[tex]x = 3.4218[/tex]

Hope this helps you :-)

Let me know if you have any other questions :-)

The set-up cost for a machine that attaches snaps on clothing is $1,100. After set-up,
it costs $0.12 for each snap to be attached. A newer machine has come out that has
a set-up cost of $1,520. With the new machine, it only costs $0.09 for each snap to
be attached. How many snaps would the company have to attach to make the
purchase of the newer machine worthwhile?

Answers

Answer:

14,001

Step-by-step explanation:

old machine: 1,100+.12x

new machine: 1,520+.09x

if you plug in 14,000 for x, you get

old machine: 2,780

new machine: 2,780

therefore, you need 1 over 14,000 for it to be worth it because

if you plug in 14,001 for x, you get

old machine: 2,780.12

new machine: 2,780.09

which makes the new machine $.03 cheaper at this point (and the more snaps attached, the more the new machine will be worth it)

hope this helps!

Find the vale of x need help

Answers

Answer:

x=45 degrees

Step-by-step explanation:

You can see based off of the markings on the 2 sides, that it is an isosceles triangle, so that means the 2 base angles are equal.

so 2x+90=180 degrees

so 2x=90 degrees

x=45  

Answer:

[tex]x=45[/tex]

Step-by-step explanation:

→a+b+c=180

→Angle a is given to be 90 degrees

→ Also the other to angles are the same length so the same angle

[tex]90+2x=180[/tex]

Step 1: Subtract 90 from both sides.  

[tex]2x+90-90=180-90[/tex]

[tex]2x=90[/tex]

Step 3: Divide both sides by 2.

[tex]\frac{2x}{2} =\frac{90}{2}[/tex]

[tex]x=45[/tex]

Answer:x=45

-2x^2 + (y)(x/3); use x= -3, and y = 2​

Answers

Answer:

-2(x^2+1)

Step-by-step explanation:

1. Divide The Numbers:

-2x^2+2(-3/3)

-2x^2+2(-1)

2. Multiply The Numbers:

-2x^2+2(-1)

-2x^2-2

3. Common Factor:

a. Factor by grouping

-2x^2+2(-3/3)

-2x^2-2

b. Factor by Grouping

-2x^2-2

-2(x^2+1)

-2x^2+(2)(-3/3)

Solution: -2(x^2 + 1)

Answer for brainliest

Answers

Answer:
If this is what your looking for, the answer may be:
-4y + 12
Hope this helps!

5x+6 ?? please help 8th grade math work

Answers

Answer:

5x + 6 = 0

5x = - 6

x = - 6/5

-6/5 is the answer

At Howard High School, 6% of the students ride bikes to school. If 950 students attend Howard High School, how many students ride a bike to school?

I need the answer like rn...

Answers

Answer:

19 students ride a bike to school

Three polygons have been divided
into triangles by drawing a
segment from one vertex to all nonadjacent vertices. If n is the
number of sides in the polygon, which expression shows the
number of triangles created by each polygon?
A.n
B.(n + 2)
C.(n - 2)
D.3n, 4n, 8n

Answers

The relationship between the sides of the polygon and the triangle follows an arithmetic sequence

The expression that represents the number of triangles is (c) n - 2

From the diagrams, we have:

Sides           Triangles

  5                    3

  6                    4

  8                    6

The above can be represented as functions as follows:

[tex]f(5) = 3[/tex]

[tex]f(6) = 4[/tex]

[tex]f(8) = 6[/tex]

Express 6 as 8 - 2

[tex]f(8) = 8 - 2[/tex]

Express 8 as n

[tex]f(n) = n - 2[/tex]

So, the expression that represents the number of triangles is (c) n - 2

Read more about sequence and patterns at:

https://brainly.com/question/24050043

Don't answer this question

Answers

Answer:

Ok

Step-by-step explanation:

How do I rewrite the improper fractions as a mixture number? Please explain step by step to get marked as brainliest

Answers

Answer:

1) Divide the numerator by the denominator.

2) Write down the whole number result.

3) Use the remainder as the new numerator over the denominator. This is the fraction part of the mixed number.

Step-by-step explanation:

not sure of this will help... but hope it does!

Answer:

Explained below :)

I tried my best to explain, sorry if it doesn't make sense

Step-by-step explanation:

Example problem: 11/4 (Mixed number)

1: 11 divided by 4 = 2 (whole number) with a remainder of 3

( Numerator divided by denominator) (Don't turn the number into a decimal leave the remainder)

2: Take the remainder and put it over the denominator 3/4

3: Whole number beside the remainder over the denominator

Your answer would be 2 3/4


At the restaurant, Gordon packed 8 orders with 4 items per order
in the morning. In the afternoon, he packed 6 orders with 7 items
per order.

Answers

Answer:

what is the question?

Step-by-step explanation:

A scientist crosses two pea plants that are

heterozygous for plant height and flower

color. Tall is dominant over short and purple is

dominant over white. The plant height and

Flower color genes are unlinked. Complete the

information below and the Punnett square.

Then answer the questions below.

Answers

The Punnett square is a diagram divided into squares that is used to determine genotypes.

The question is incomplete, as the required details such as the characters that represent the plant heights and the flower colors are not given.

So, I will give a general explanation instead.

Assume the plants that are crossed are represented as: TT and Tt.

The possible genotypes would be TT, TT,Tt and Tt

In the above list of genotypes, genotype T is dominant over genotype t

See attachment for an illustration of the Punnett square.

Read more about Punnett square at:

https://brainly.com/question/15723456

Out of 250 million cars on the road in US, about 3.5% are diesel. What percentage are not diesel?

Answers

Answer:

96.5%

Step-by-step explanation:

Answer:

241250000 cars aren't diesel (Basically 96.5%)

Step-by-step explanation:

250 million = 250000000

If we are talking about the percentage of cars that aren't diesel, we have two ways of solving this. (I'm gonna solve for not just percentage but for amount too)

1. Find out the percentage that isn't diesel by subtracting 3.5% from 100% and then multiplying the answer to get the result.

or

2. We find out what 3.5% of 250 million is and then subtract that from 250 million

Now to make this short, I will do the first one.

100-3.5 = 96.5

96.5% x 250,000,000 = 241250000

Given p(x) = x4 – 13x2 – 25x – 12.

A) Use long division to determine the remainder when p(x) is divided by (x2 – 4)? Show all of your work for full credit.

B) Use mathematical methods to prove that your quotient and remainder are correct. Show all of your work for full credit.

Answers

Answer:

Below.

Step-by-step explanation:

p(x) = x^4 - 13x^2 – 25x – 12

Long division:

x^2 - 4)x^4 - 13x^2 – 25x – 12( x^2 - 9  <-------- Quotient

           x^4 -  4x^2

Subtract:       -9x^2 -  25x

                     -9x^2  + 36

                                 -25x - 36 - 12

So the remainder is -25x - 48 (Answer).

B)   If the above are correct then:

(x^2 - 4) * quotient + remainder  = the original form of  p(x).

(x^2 - 4)(x^2 -9)  - 25x - 48 = the original p(x).

p(x) = x^4 - 9x^2 - 4x^2 + 36  - 25x - 48

= x^4 - 13x^2 - 25x -12 = original p(x)

                   

if EF = 8x + 16, FG = 60, and eg = 156, find the value of x​

Answers

Answer:

10

Step-by-step explanation:

8x+16+60=156

8x+76=156

8x=80

x=10

84/120 equivalent fraction

Answers

Answer:

7/10

this should work

Step-by-step explanation:

Captain Brewster captured a pack of aliens. The following data points represent the lengths of each of the aliens' big toes (in centimeters). 18, 16, 17, 17, 16, 15, 16. Using this date, create a dot plot where each dot represents a big toe.

Answers

Answer:

15 ·

16 ···

17 ··

18 ·

19

Step-by-step explanation:

There were 2 aliens that each have big toes measuring 17 cm long. So, the 17 would have 2 dots above it:

17 ··

What is the 24th term in the sequence 1, 3, 5, 7

Answers

Answer:

47

Step-by-step explanation:

Each new term is the previous term +2.

1st term = 1

5th term = 9

10th term = 19

15th term = 29

20th term = 39

25th term = 49 - 2 = 47 = 24th term

Help help math math math

Answers

Answer:

10000

Step-by-step explanation:

you have four digits and each one of them can be 0-9, so 10 possibilities for each digit

10×10×10×10= 10,000

Answer:

160

Step-by-step explanation:

I believe the answer is 160 because it is a four-digit passcode, and 10 different numbers can be used ( 10 * 4 = 40, and 40 * 4 = 160).


An elevator company claims "for every 15 inches of cable, we can hold up to 32 pounds". Each elevator comes with a standard length of 18 inches for their cable. If an elevator has a
weight limit of 800 lbs, how many additional inches of cable were used?

Answers

375 inches of cable were used for an elevator with weight limit of 800 lbs

Let y represent the weight in pounds and x represent the inches of cable.

Since y and x are proportional:

y = kx,

k is the constant of proportionality.

15 inches of cable, we can hold up to 32 pounds. Hence:

32 = 15k

k = 2.13 pounds per inch

y = 2.13x

For a weight of 800 lbs, y= 800:

800 = 2.13x

x = 375 inches

375 inches of cable were used for an elevator with weight limit of 800 lbs

Find out more on equation at: https://brainly.com/question/2972832

Evaluate. Express your answer in scientific notation.
4.36 x 104 – 41, 600

Answers

Answer: 3.456 × 1011

Step-by-step explanation:

Other Questions
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