JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
If for some \(\alpha, \beta ; \alpha \leq \beta, \alpha+\beta=8\) and \(\sec ^2\left(\tan ^{-1} \alpha\right)+\operatorname{cosec}^2\left(\cot ^{-1} \beta\right)-36\), then \(\alpha^2+\beta\) is_______.
- A 10
- B 12
- C 14
- D 16
Answer & Solution
Correct Answer
(C) 14
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Let } \tan ^{-1} \alpha=A \Rightarrow \tan A=\alpha \\ & \cot ^{-1} \beta=B \Rightarrow \cot B=\beta \\ & \sec ^2 A+\operatorname{cosec}^2 B=36 \\ & \Rightarrow 1+\tan ^2 A+1+\cot ^2 B=36 \\ & \Rightarrow \alpha^2+\beta^2=34 \end{aligned}\) Also…
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