[tex]\frac{cos^2x + sin^2x}{cot^2x - cosec^2x} = -1[/tex]
Solution:
Given trignometric expression is:
[tex]\frac{cos^2x + sin^2x}{cot^2x - cosec^2x}[/tex]
We have to evaluate the above expression
Let us use the trignometric identities
[tex]sin^2x + cos^2x = 1[/tex]
Also, use another trignometric identitiy
[tex]1 + cot^2x = cosec^2x[/tex]
Therefore, upon rearranging we get,
[tex]cot^2 x -cosec^x = -1[/tex]
Apply these two identities in given expression
[tex]\frac{cos^2x + sin^2x}{cot^2x - cosec^2x} = \frac{1}{-1}\\\\\frac{cos^2x + sin^2x}{cot^2x - cosec^2x} = -1[/tex]
Thus value of given expression is -1
