If and y = ( 1 2 ^ -1 ( x 2 ) ) then which of the following statements holds good ?

MATHEMATICS · Single correct · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

If x=2cos⁡−1(12)+sin⁡−1(12)+tan⁡−1(3)x = 2 \cos^{-1}\left(\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{\sqrt{2}}\right) + \tan^{-1}(\sqrt{3}) and y=cos⁡(12sin⁡−1(sin⁡x2)) then which of the followingy = \cos\left(\frac{1}{2} \sin^{-1}\left(\sin \frac{x}{2}\right)\right) \text{ then which of the following} statements holds good ? (a) y=cos⁡3π16y = \cos \frac{3\pi}{16} (b) y=cos⁡5π16y = \cos \frac{5\pi}{16} (c) x=4cos⁡−1yx = 4 \cos^{-1} y (d) none of these

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