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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 _______________.

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

 

answered Feb 18, 2013 by thanvigandhi_1
edited Mar 16, 2013 by thanvigandhi_1
 
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