Solve the following equations.
$2 cos x sin 3 x = sin 4 x + 1.$

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Solution

$2 cos x sin 3 x - sin 4 x = 1$
$sin 4 x + sin 2 x - sin 4 x = 1$
$sin 2 x = 1, 2 x = n π + {- 1}^{n} \frac{π}{2}, x = n \frac{π}{2} + {(- 1)}^{n} \frac{π}{4} .$

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