Let fk(x) = ${1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)$ for k = 1, 2, 3, ... Then for all x $ \in $ R, the value of f4(x) $-$ f6(x) is equal to

Question

Let f_k(x) = ${1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)$ for k = 1, 2, 3, ... Then for all x $ \in $ R, the value of f₄(x) $-$ f₆(x) is equal to

${1 \over 4}$

${5 \over {12}}$

${{ - 1} \over {12}}$

${1 \over {12}}$

Solution

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