Find the principal value of each of the following :

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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