Which of the following is/are true?

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Which of the following is/are true? (a) dydx\frac{dy}{dx} for y=sin⁡−1(cos⁡x)y=\sin^{-1}(\cos x), where x∈(0,π)x\in(0,\pi), is −1-1 (b) dydx\frac{dy}{dx} for y=sin⁡−1(cos⁡x)y=\sin^{-1}(\cos x), where x∈(π,2π)x\in(\pi,2\pi), is 11 (c) dydx\frac{dy}{dx} for y=cos⁡−1(sin⁡x)y=\cos^{-1}(\sin x), where x∈(−π2,π2)x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right), is −1-1 (d) dydx\frac{dy}{dx} for y=cos⁡−1(sin⁡x)y=\cos^{-1}(\sin x), where x∈(π2,3π2)x\in\left(\frac{\pi}{2},\frac{3\pi}{2}\right), is −1-1

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