Question:
Find the principal value of each of the following :
$\sin \left(\sec ^{-1} x+\operatorname{cosec}^{-1} x\right)$
Solution:
$\sin \left(\sec ^{-1} x+\operatorname{cosec}^{-1} x\right)=\sin \left(\frac{\pi}{2}\right)$ [Formula: $\sec ^{-1} x+\operatorname{cosec}^{-1} x=\frac{\pi}{2}$ ]
Putting the value of $\sin \left(\frac{\pi}{2}\right)$
$=1$
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