The value of $-cosec^2(\cot^{-1}y) + \sec^2 (\tan^{-1}x)$ is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $x^2 - y^2$
Given expression:
$- \csc^2(\cot^{-1}y) + \sec^2(\tan^{-1}x)$
Using identities:
$\sec^2(\tan^{-1}x) = 1 + x^2$
$\csc^2(\cot^{-1}y) = 1 + y^2$
Substitute:
$- (1 + y^2) + (1 + x^2)$
$= -1 - y^2 + 1 + x^2$
$= x^2 - y^2$
Therefore, the value is $x^2 - y^2$.