Question

Cos^2x+sin^2x/cot^2x-csc^2x

Answer 1

$\frac{cos^2x + sin^2x}{cot^2x - cosec^2x} = -1$

Solution:

Given trignometric expression is:

$\frac{cos^2x + sin^2x}{cot^2x - cosec^2x}$

We have to evaluate the above expression

Let us use the trignometric identities

$sin^2x + cos^2x = 1$

Also, use another trignometric identitiy

$1 + cot^2x = cosec^2x$

Therefore, upon rearranging we get,

$cot^2 x -cosec^x = -1$

Apply these two identities in given expression

$\frac{cos^2x + sin^2x}{cot^2x - cosec^2x} = \frac{1}{-1}\\\\\frac{cos^2x + sin^2x}{cot^2x - cosec^2x} = -1$

Thus value of given expression is -1