A function satisfies f(x)= x+ _0^x f'(t)(2 t- ^2 t) ,dt

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

A function f(x)f(x) satisfies f(x)=sin⁡x+∫0xf′(t)(2sin⁡t−sin⁡2t) dt.f(x)=\sin x+\int_0^x f'(t)(2\sin t-\sin^2 t)\,dt. Then f(x)f(x) is: (1) x1−sin⁡x\frac{x}{1-\sin x} (2) sin⁡x1−sin⁡x\frac{\sin x}{1-\sin x} (3) 1−cos⁡xcos⁡x\frac{1-\cos x}{\cos x} (4) tan⁡x1−sin⁡x\frac{\tan x}{1-\sin x}

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