Question

The general solution of the equation $2{\cos }^{2}x=-3\sin x$ is

• A. $x=n\pi +\frac{7\pi }{6},n\in Z$
• B. $x=n\pi +(-1{)}^n\frac{7\pi }{6},n\in Z$
• C. $x=n\pi +(-1{)}^n\frac{\pi }{6},n\in Z$
• D. $x=n\pi +\frac{\pi }{6},n\in Z$

Answer 1

The correct option is B $x=n\pi +(-1{)}^n\frac{7\pi }{6},n\in Z$

$2{\cos }^{2}x=-3\sin x$
$\Rightarrow 2{\sin }^{2}x-3\sin x-2=0$
$\Rightarrow (2\sin x+1)(\sin x-2)=0$
$\Rightarrow \sin x=\frac{-1}{2}[\because \sin x-2\ne 0]$
$\Rightarrow \sin x=\sin \frac{7\pi }{6}$
$\Rightarrow x=n\pi +(-1{)}^n\frac{7\pi }{6},n\in Z$