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Q.

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

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a

12

b

5

c

15

d

9

answer is C.

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Detailed Solution

$\begin{array}{l} \sec^{2} (\tan^{- 1} 2) + {cosec}^{2} (\cot^{- 1} 3) \\ = {[\sec (\tan^{- 1} 2)]}^{2} + {[cosec (\cot^{- 1} 3)]}^{2} \\ = {[\sec (\sec^{- 1} \sqrt{5})]}^{2} + {[cosec ({cosec}^{- 1} \sqrt{10})]}^{2} \\ = (\sqrt{5})^{2} + (\sqrt{10})^{2} = 5 + 10 = 15 \end{array}$

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The value of sec2⁡tan−1⁡2+cosec2⁡cot−1⁡3 is