JEE-Mains 2014 (28/30)

Geometry Level 2

Let fk(x)=1k(sinkx+coskxf_k(x)=\frac{1}{k} (\sin^kx+\cos^kx) where xRx \in \mathbb{R} and k1k \geq 1. What is the value of f4(x)f6(x)f_4(x)-f_6(x)?

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