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  4. If tan -1(-α+θ-(θ3/3 !)+(θ5/5 !)-(θ7/7 !)+ ldots . . ∞)+ cot -1(α-1+(θ2/2 !)-(θ4/4 !)+ ldots ldots)=(π/2) then maximum value of α equals to -

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

Inverse Trigonometric Functions

Solution:

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