ત્રિકોણમિતીય પ્રતિવિધેયો — ગણિત ધોરણ 12 સાયન્સ — Question

‎ $sin^{-1} \left(\frac{sin x + cos x}{\sqrt{2}}\right)$

$= sin^{-1} \left(\frac{1}{\sqrt{2}}sin x + \frac{1}{\sqrt{2}} cos x\right)$

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

$= sin^{-1} \left(sin \left(\frac{\pi}{4} + x\right)\right)$

$= \frac{\pi}{4} + x\ \begin{cases}\frac{-\pi}{4} < x <\frac{\pi}{4} &\\\frac{\pi}{4}-\frac{\pi}{4} < x < \frac{\pi}{4}+\frac{\pi}{4}&\end{cases}$

$0 < \frac{\pi}{4} + x < \frac{\pi}{2}$