The number of solutions of $\sin^{7} x + \cos^{7} x = 1$ , $x \in [0, 4 π]$ is

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answer is C.

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Detailed Solution

$\sin^{7} x + \cos^{7} x = 1$ is possible when $\begin{array}{l} \sin x = 0, \cos x = 1 \Rightarrow x = 0, 2 π, 4 π \\ o r \sin x = 1, \cos x = 0 \Rightarrow x = \frac{π}{2}, \frac{5 π}{2} \end{array}$

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