If , where and , then is equal…

MATHEMATICS · Single correct · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

If fk(x)=1k(sin⁡kx+cos⁡kx)f_k(x)=\frac{1}{k}(\sin^k x+\cos^k x), where x∈Rx\in\mathbb{R} and k≥1k\geq1, then f4(x)−f6(x)f_4(x)-f_6(x) is equal to (1) 16\frac{1}{6} (2) 13\frac{1}{3} (3) 14\frac{1}{4} (4) 112\frac{1}{12}

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