trigonometry .. please help!?

Question

Verify that the equation is an identity . Please show me the steps.
( 1+ cos x / 1-cos x) - ( 1 - cos x / 1+ cos x) = 4 cot x csc x


find the exact value of sin ( A + B)
* sin A = 3/5 and cos A is negative
* sin B = 8/17 and tan B is negative

Answer 1

( 1+ cos x )/( 1-cos x) - ( 1 - cos x) /( 1+ cos x)
= [(1+cos x)^2 - (1-cos x)^2]/sin^2 x
= 4cos x/sin^2 x
= 4cot x csc x
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Ideas: The common denominator is 1-cos^2 x = sin^2 x.

sin ( A + B)
= sinAcosB+cosAsinB
= (3/5)(-15/17)+(-4/5)(8/17)
= -77/85
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Ideas: Both A and B are in the second quadrant because of positive sine and negative cosine.

Answer 2

LHS = ( 1+ cos x / 1-cos x) - ( 1 - cos x / 1+ cos x)
= [ (1+cos x)^2 / (1 - cos x )(1+ cosx) ] - [ (1-cos x)^2 / (1 - cos x )(1+ cosx) ]
= [ (1+cos x)^2 - (1 - cos x)^2 ] / (1- cos^2 x)
= (1 + 2cos x + cos^2 x - 1 + 2cos x - cos^2 x ) / sin^2 x
= 4cos x / sin^2 x
= 4 cot x csc x
=RHS

sin A = 3/5 and cos A is negative. This shows that A is in the 2nd quadrant and cos A= -4/5

sin B = 8/17 and tan B is negative.This shows that B is in the 2nd quadrant and cos B = -15/17

sin (A+B) = sin A cos B + cos A sin B
=(3/5)(-15/17) + (-4/5)(8/17)
= - 77/85

Answer 3

LHS
= N / D
Where N is given by:-
(1 + cos x) (1 + cos x) - (1 - cos x) (1 - cos x)
1 + 2 cos x + cos ² x - (1 - 2 cos x + cos ² x)
4 cos x

D is given by:-
(1 - cos x)(1 + cos x)
1 - cos ² x
sin ² x

N / D is given by:-
4 cos x / sin ² x
4 (cos x / sin x) (1 / sin x)
4 cot x cosec x

RHS
4 cot x cosec x

LHS = RHS

Answer 4

hmm....looks like you need to call mr. Albert Einstien.
lol