Let be such that then equals

MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals

Problem

Let ddxf(x)=sin⁡12x−cos⁡12x(sin⁡2x−cos⁡2x)(1−3sin⁡2xcos⁡2x)\frac{d}{dx} f(x) = \frac{\sin^{12} x - \cos^{12} x}{(\sin^2 x - \cos^2 x)(1 - 3 \sin^2 x \cos^2 x)} be such that f(0)=0f(0) = 0 then f(π2)f\left(\frac{\pi}{2}\right) equals kπ16\frac{k\pi}{16}. Find the value of k (k∈N)k\,(k \in \mathbb{N})

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