Evaluate: ( ^ -1 3 4 + ^ -1 4 3 ) - Vidyadip

Question

Evaluate:
$\cot\Big(\sin^{-1}\frac{3}{4}+\sec^{-1}\frac{4}{3}\Big)$

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Answer

$\cot\Big(\sin^{-1}\frac{3}{4}+\sec^{-1}\frac{4}{3}\Big)$
$=\cot\Big(\sin^{-1}\frac{3}{4}+\cos^{-1}\frac{3}{4}\Big)$ $\Big[\because\ \sec^{-1}\text{x}=\cos^{-1}\frac{1}{\text{x}}\Big]$
$=\cot\Big(\frac{\pi}{2}\Big)$ $\Big[\because\ \sin^{-1}\text{x}+\cos^{-1}\text{x}=\frac{\pi}{2}\Big]$
$=0$

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