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  4. cot-1 [(cos α)(1/2)] + tan-1[(cos α)(1/2)] = x then sin x =

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Q. $cot^{-1} [(cos\,\alpha)^{\frac{1}{2}}] + tan^{-1}[(cos\,\alpha)^{\frac{1}{2}}] = x$ then $sin\,x = $

Inverse Trigonometric Functions

Solution:

Using $tan^{-1} \theta + cot^{-1} \theta = \frac{\pi}{2} =x$
$\therefore sin\,x - sin \frac{\pi}{2} -1$