^2 ( ^ - 1 2) + cose c ^2 ( ^ - 1 3) = - Vidyadip

MCQ

${\sec ^2}({\tan ^{ - 1}}2) + {\rm{cose}}{{\rm{c}}^2}({\cot ^{ - 1}}3) = $

A
$5$
B
$13$
✓
$15$
D
$6$

✓

Answer

Correct option: C.

$15$

c
(c) Let ${\tan ^{ - 1}}2 = \alpha \Rightarrow \tan \alpha = 2$

and ${\cot ^{ - 1}}3 = \beta \Rightarrow \cot \beta = 3$

${\sec ^2}({\tan ^{ - 1}}2) + {\rm{cose}}{{\rm{c}}^{\rm{2}}}({\cot ^{ - 1}}3)$

$= {\sec ^2}\alpha + {\rm{cose}}{{\rm{c}}^{\rm{2}}}\alpha $

$=1 + {\tan ^2}\alpha + 1 + {\cot ^2}\alpha $

$= 2 + {(2)^2} + {(3)^2} = 15$.

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