If , then is increasing…

MATHEMATICS · Multi correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

If f(x)=tan⁡−1(sin⁡x+cos⁡x)f(x)=\tan^{-1}(\sin x+\cos x), then f(x)f(x) is increasing in: (1) (−π2,π4)\left(-\frac{\pi}{2},\frac{\pi}{4}\right) (2) (−π4,π4)\left(-\frac{\pi}{4},\frac{\pi}{4}\right) (3) (5π4,3π2)\left(\frac{5\pi}{4},\frac{3\pi}{2}\right) (4) (−2π,−7π4)\left(-2\pi,-\frac{7\pi}{4}\right)

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