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If \(-\frac{\pi}{4} < x < \frac{\pi}{4}\) , then value of \(sin^{-1} (\frac{sinx + cosx}{\sqrt2})\) is equal to(A) x + π(B) x + π/4(C) x + π/2(D) x + 2π |
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Answer» Correct option is (B) x + \(\frac{\pi}4\) sin-1(\(\frac{sin x+cos x}{\sqrt2}\)) ; \(\frac{\pi}4<x<\frac{\pi}4\) = sin-1(sin x cos\(\frac{\pi}4\) + cos x sin \(\frac{\pi}4\)) = sin-1(sin (x + \(\frac{\pi}4\))); 0 < x + \(\frac{\pi}4\) < \(\frac{\pi}2\) = x + \(\frac{\pi}4\) |
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