Write an identity in terms of sines and cosines to simplify

Write an identity in terms of sines and cosines to simplify it. The expression 1 + cot^2 x/1 - CSC^2 x simplifies to sin x cos x 1 - cos^2 x tan^2 x + 1 -sec^2z sin x tan x sec x

Solution

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

we know cotx = cosx/sinx ; cscx = 1/sinx

(1+cot^2x)/( 1-csc^2x) = ( cos^2x +sin^2x)/(sin^2x -1)
=1/(-cos^2x)

= -sec^2x

OPtion : -sec^2x