Solve:- $sin 2 x + cos x = 0$

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Solution

We know that $sin 2 x = 2 sin x cos x$

So this becomes,

$2 sin x cos x + cos x = 0$

$(2 sin x + 1) (cos x) = 0$

$(2 sin x + 1) = 0 \Rightarrow sin x = \frac{- 1}{2} \Rightarrow x = \frac{7 π}{6}$

$cos x = 0 \Rightarrow cos x = 0 \Rightarrow x = \frac{π}{2}$

So, $x = \frac{7 π}{6}, \frac{π}{2}$

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