Differentiate `sin^(-1){(sinx+cosx)/(sqrt(2))},\ -(3pi)/4

Explanation

Solution:

Let `y=\sin ^{-1}\{\frac{\sin x+\cos x}{\sqrt{2}}\}`

`Rightarrow y=\sin ^{-1}\{(\sin x \cdot \frac{1}{\sqrt{2}}+\cos x \cdot \frac{1}{\sqrt{2}})\}`

`Rightarrow y=\sin ^{-1}\{(\sin x \frac{\cos \pi}{4}+\cos x \frac{\sin \pi}{4})\}`

As, `\sin A \cos B+\cos A \sin B=\sin (A+B)`

`\therefore y=\sin ^{-1}\{(\sin (x+\frac{\pi}{4})\}.`

As, `-\frac{3 \pi}{4}
`\therefore-\frac{\pi}{2}
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