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.

1. 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