Maths. Section B1Inverse Trigonometric Functions

The value of tan^2 (sec^-12)+ cot^2(cosec^-13) is equal to

The value of $\tan^2 (\sec^{-1}2)+ \cot^2(\mathrm{cosec}^{-1}3)$ is equal to

Answer & explanation

Correct answer: option 2

The correct answer is Option (2) → 11

Let $\theta = \sec^{-1}2$ and $\phi = \mathrm{cosec}^{-1}3$, so $\sec\theta = 2$ and $\mathrm{cosec}\,\phi = 3$. By the Pythagorean identities $\tan^2\theta = \sec^2\theta - 1$ and $\cot^2\phi = \mathrm{cosec}^2\phi - 1$:

$\tan^2(\sec^{-1}2) = 2^2 - 1 = 3$
$\cot^2(\mathrm{cosec}^{-1}3) = 3^2 - 1 = 8$

$3 + 8 = 11$

NCERT Exemplar:
Inverse Trigonometric Functions

$NCERT extract$