Write an identity in terms of sines and cosines to simplify

Write an identity in terms of sines and cosines to simplify it. Select the expression that completes the identity 1 + sin^2 x = 1/cos^2 csc^2 x - sec^2 x sin^2 x + cot^2 x - csc^2 x cos^2 x csc^2 x - cot^2 x + sin^2 cos^2 x - 1

Solution

1+ sin^2x

we know that 1+cot^2x = csc^2x

So, 1 = csc^2x -cot^2x

So,1+ sin^2x = (csc^2x -cot^2x) +sin^2x

= csc^2x -cot^2x +sin^2x

Option 5 : csc^2x -cot^2x +sin^2x