All categories

3 years ago

Verify the following identity: (csc theta -cot theta )/(sec theta -1) A. sec theta B. cos theta C. cot theta D. sin theta

Mathematics

1 answer:

alexdok [17]3 years ago

3 0

Answer:

C. cot theta

Step-by-step explanation:

(csc theta -cot theta )/(sec theta -1)

csc = 1/ sin

cot = cos / sin

sec = 1 / cos

Let x = theta

(1/ sin x -cos x / sin x )/(1/ cos x -1)

Getting a common denominator in the denominator and combining terms

(1- cos x)/ sinx / ( 1 - cos x) / cos x

(1- cosx) (1- cosx)

----------- ÷ ------------

sinx cos x

Copy dot flip

(1- cosx) cosx

----------- * ------------

sinx 1 -cos x

Cancel like terms

cos x / sin x

cos / sin = cot

cot x

cot theta

You might be interested in

Please answer as many as you can from problems 2-8

klasskru [66]

W0W alot........
2. 16/5c
3. 3q/2r^2
4. 1
5. yw^2/z^3x^3
6. 20j
7. 0 + m^2-m+m+1/m^2-m
8. 1- 1/b+2
H0P3 It H3LPS :)
#Itwashardwork

3 0

3 years ago

Pat's income is 20 % more than Adam. How much percent is Adam's income less than Pat's?

pantera1 [17]

Answer: 20%

Step-by-step explanation: The same number applies here. Think about it this way, let's say you have a friend named Sofia and she has 3 dollars more than you, how many dollars do you have less than Sofia? 3 dollars. That's the easiest way I can explain it.

4 0

3 years ago

Does 4(2x-5) equal 8x-5 or 8x-20? explain

Scorpion4ik [409]

4(2x-5)
8x-20

it is equal to 8x-20 because you simplify it and it turns into that.
HOPE I HELPED!!!

8 0

3 years ago

Read 2 more answers

Work out the size of the angle X.<br><br> Give your answer correct to 3 significant figures.

aleksley [76]

Step-by-step explanation:

Recall the Ratio for tan

Tan(theta) = opposite / adjacent

Tan (x) = 9 / 5

solve for x (use Tan^-1(...) )

3 0

2 years ago

Read 2 more answers

List the sides of each triangle from shortest to greatest

Lelechka [254]

In every triangle, the largest side, is opposite the largest angle.

Also, the smallest side, is opposite the smallest angle.

a. $70^o\ \textgreater \ 60^o\ \textgreater \ 50^o$ so $|RQ|\ \textgreater \ |PR|\ \textgreater \ |PQ|$ ,

because RQ is opposite angle P, the largest,
PR is opposite angle Q , the middle
and PQ is opposite angle R, the smallest.

Greatest side: RQ

b. The sum of the measures of the interior angles of any triangle is 180°,

so

$m(A)+m(B)+m(C)=180^o\\\\50^o+45^o+x=180^o\\\\x=180^o-50^o-45^o=85^o$

thus, m(C) is the largest angle. This means the largest side is the side AB.

Answers:

a) RQ
b)AB

8 0

3 years ago