If and ^ -1 y - ^ -1 ( x 1+x^2 ) = 6

MATHEMATICS · Subjective · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

If tan⁡−1x+tan⁡−11−y2y=π3\tan^{-1} x + \tan^{-1} \frac{\sqrt{1-y^2}}{y} = \frac{\pi}{3} and sin⁡−1y−cos⁡−1(x1+x2)=π6, then 5sin⁡−1xsin⁡−1y is\sin^{-1} y - \cos^{-1}\left(\frac{x}{\sqrt{1+x^2}}\right) = \frac{\pi}{6}, \text{ then } \frac{5 \sin^{-1} x}{\sin^{-1} y} \text{ is}

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