JEE-Mains 2014 (28/30)

Geometry Level 2

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

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