Solve: $sin x + sin 2 x = cos x + 2 {cos}^{2} x .$

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Solution

$s i n x + 2 s i n x c o s x = c o s x + 2 c o s^{2} x$
$s i n x (1 + 2 c o s x) = c o s x (1 + 2 c o s x)$
$⟹ x = π / 4, π / 3$

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