Total number of solution(s) of the equation $sin 4 x + cos 4 x = 2$ in $[- 2 π, 2 π]$ is :

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Solution

$sin 4 x + cos 4 x = 2$
$∵ sin 4 x \leq 1$ and $cos 4 x \leq 1$
So, it is possible only, when
$sin 4 x = 1$ and $cos 4 x = 1$
Which is not possible as ${sin}^{2} θ + {cos}^{2} θ = 1$
$\Rightarrow$ Hence, there is no solution.

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