Question

If ${\tan }^{-1}\left(-\alpha +\theta -\frac{{\theta }^3}{3!}+\frac{{\theta }^5}{5!}-\frac{{\theta }^7}{7!}+\dots ..\infty \right)+{\cot }^{-1}\left(\alpha -1+\frac{{\theta }^2}{2!}-\frac{{\theta }^4}{4!}+\dots \dots \right)=\frac{\pi }{2}$ then maximum value of $\alpha$ equals to -

• A. $-\frac{1}{\sqrt{2}}$
• B. 1
• C. $\frac{1}{2}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

Answer: (D)

Correct answer is (d) $\frac{1}{\sqrt{2}}$