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  • The value expression tan into bracket sin inverse x plus cos inverse x divided 2 when x equal to square root divided 2 is

The value of expression \tan\left ( \frac{\sin^{-1}x+\cos^{-1}x }{2}\right ), when x=\frac{\sqrt{3}}{2} is___________.

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The value of expression \tan\left ( \frac{\sin^{-1}x+\cos^{-1}x}{2} \right ) When X=\frac{\sqrt{3}}{2} is 1

\tan\left ( \frac{\sin^{-1}x+\cos^{-1}x}{2} \right ) When X=\frac{\sqrt{3}}{2}

We know that, (sin–1 x + cos–1 x) for all |x| ≤ 1 is \frac{\pi}{2}

As,  x=\frac{\sqrt{3}}{2} lies in domain

So \tan\left ( \frac{\sin^{-1}x+\cos^{-1}x}{2} \right )=\tan \frac{\pi}{4}

=1

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