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# The value of expression $\tan\bigg(\Large \frac{\sin^{-1}x+\cos^{-1}x}{2} \normalsize\bigg),when\;x=\frac{\sqrt 3}{2}$ is _______________.

Toolbox:
• $sin^{-1}x+cos^{-1}x=\large\frac{\pi}{2}$ for all x
• $tan\large\frac{\pi}{4}=1$
Ans: 1

Since $sin^{-1}x+cos^{-1}x=\large\frac{\pi}{2}$ for all x,
$tan\bigg(\large\frac{sin^{-1}x+cos^{-1}x}{2}\bigg)=tan\big(\large\frac{\frac{\pi}{2}}{2}\big)$
$=tan\large\frac{\pi}{4}=1$

edited Mar 16, 2013