Trigonometry verifying identities. Verify ! (sin x tan x) =cos x csc^2 x / cot^2 x + cot^4 x?

Question

This is for you math_kp . Are you gonna be online over the weekend if I have questions with homework ?

Answer 1

sin(x)tan(x)=(cos(x)csc^2(x))/(cot^2(x)+cot^4(x))
Step 1. Starting with the right side (the obviously more complicated one) factor out a cotangent squared out of the denominator.

(cos x csc^2 x)/ cot^2 x (1+cot^2 x)

Step 2. Use the identity csc^2 x= cot^2 x+1 in the numerator and separate the cosine x in the top and the cotangent squared x in the bottom

(cosx/cot^2 x) * (cot^2 x+1/ cot^2 x +1)

Step 3. This leaves you with a cosine x divided by cotangent squared x times 1. Use the identity that says cot x = cos x/ sin x

(cos x) / (cos^2 x/ sin^2 x)

Step 4. Divide the double fraction and get

(sin^2 x cosx)/ (cos^2 x)

Step 5. Separate your multiple factors from the squares and separate the fraction into three parts, one will be the sine x, the other will be the tangent x (because tan x = sin x/ cos x), and the cosine x divided by cosine x will go to 1.

sin x * (sin x/ cos x) *(cos x/ cos x)

Step 6. Write final answer

sin x tan x = sin x tan x

Answer 2

I shall not be on line. However I shall acess questions once a while.

coming back to the problem

RHS is more complex so start from RHS
numerator cos x csec^2 x
denominator = cot^2 x + cot ^4 x
= cot ^2 x( 1+ cot^2 x)
= cot ^2 x . cosec ^2 x

now ratio = cos x/cot^2 x
= cos x tan ^2 x as cot^2 x = 1/tan ^2 x
= (cos x tan x) tan x
= sinx tan x
= RHS
steps in general should be
1) start from more complex side
2) do not distrub the terms which is same as othe side

Answer 3

(sin x tan x) =? cos x csc^2 x / cot^2 x + cot^4 x
(sin x tan x) =? cos x csc^2 x / cot^2 x(1 + cot^2x)
(sin x tan x) =? cos x csc^2 x / cot^2 xcsc^2x
(sin x tan x) =? cos x / cot^2x
(sin x tan x) =? cos x sin^2 x/cos^2 x
(sin x tan x) =? cos xsin x tan x /cos x
(sin x tan x) = sin x tan x

Answer 4

Csc means cosecant for the person who asked. it's sin^(-1). I did all this last year but it's horrible and proofs take forever and I'd rather not type it all out. Good luck.

-Lena

Answer 5

cos x - cos x / (a million- tan x) = sin x cos x / (sin x - cos x) Taking the left hand area: cos x - cos x / (a million- tan x) = cos(x)[a million-tan(x)]/(a million-tan(x)) - cos(x)/(a million - tan(x)) = [cos(x)[a million - tan(x)] - cos(x)]/(a million - tan(x)) = cos(x)[a million - tan(x) - a million]/(a million - tan(x)) = cos(x)[-tan(x)]/[a million - tan(x)] = - sin(x)/[a million - tan(x)] = - sin(x)cos(x)/[cos(x)(a million - tan(x))] = - sin(x)cos(x)/[cos(x) - sin(x)] = sin(x)cos(x)/(sin(x) - cos(x)) = suited hand area. subsequently shown.

Answer 6

csc = ? what does it mean ?