Write the expression in terms of sines and cosines and simpl

Write the expression in terms of sines and cosines and simplify so the answer is NOT a quotient. Select the expression that completes the identity 1/1 + cos x - 1/1 - cos x = 1/1 - cos^2 x -2 sin x middot sec^2x -2 cot x middot csc x 0 - 2 cos x/sin^2 x csc^2 x

Solution

1/(1 +cosx) -1/(1-cosx)

( 1 -cosx -( 1 +cosx) )/( 1 -cos^2x)

= -2cosx/sin^2x    { we know that sin^2x +cos^2x =1 }

= -2cotx*cscx