Aspire Faculty ID #18345 · Topic: AMU MCA 2017 · Just now
AMU MCA 2017

If $\sin^{-1} x - \cos^{-1} x = \frac{\pi}{6}$, then the value of $x$ is:

Solution

Given, $\sin^{-1} x - \cos^{-1} x = \frac{\pi}{6}$ — (i)We know the identity: $\sin^{-1} x + \cos^{-1} x = \frac{\pi}{2}$ — (ii)Adding equations (i) and (ii):$(\sin^{-1} x - \cos^{-1} x) + (\sin^{-1} x + \cos^{-1} x) = \frac{\pi}{6} + \frac{\pi}{2}$$2\sin^{-1} x = \frac{\pi + 3\pi}{6}$$2\sin^{-1} x = \frac{4\pi}{6}$$2\sin^{-1} x = \frac{2\pi}{3}$$\sin^{-1} x = \frac{\pi}{3}$$x = \sin\left(\frac{\pi}{3}\right)$$x = \frac{\sqrt{3}}{2}$
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