Question

Find the principal solutions of sin 2x + cos x = 0

• A. $x=-\frac{\pi }{3}$, $x=\frac{\pi }{3}$
• B. $x=-\frac{\pi }{6}$, $x=\frac{\pi }{2}$
• C. $x=\frac{\pi }{3}$
• D. $x=\frac{\pi }{2}$

Answer 1

The correct option is B

$x=-\frac{\pi }{6}$, $x=\frac{\pi }{2}$

sin 2x + cos x=0
2sin x cos x + cos x = 0
cos x(2sin x + 1) = 0
cos x = 0 or sin x = -$\frac{1}{2}$
x = $\frac{\pi }{2}$ or x = -$\frac{\pi }{6}$