Find the general solution of $4 sin x cos x + 2 sin x + 2 cos x + 1 = 0$

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Solution

$4 s i n x c o s x + 2 s i n x + 2 c o s x + 1 = 0$

$2 s i n x (2 c o s x + 1) + 1 (2 c o s x + 1) = 0$

$(2 c o s x + 1) (2 s i n x + 1) = 0$

$c o s x = \frac{- 1}{2} (o r) s i n x = \frac{- 1}{2}$

$x = {- 30}^{o} o r 120^{o}$

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