Question

Number of solution of x in $[0,3\pi ]$ satisfying $\sqrt{6-sinx-7{cos}^{2}x}+sinx=0$

• A. 0
• B. 2
• C. 4
• D. 6

Answer 1

Answer: (B)

2

Given,

$\sqrt{6-\sin x-7{\cos }^{2}x}+\sin x=0$

$\sqrt{6-\sin x-7{\cos }^{2}x}=-\sin x$

$6-\sin x-7{\cos }^{2}x={\sin }^{2}x$

$6-\sin x-7(1-{\sin }^{2}x)={\sin }^{2}x$

$6-\sin x-7+7{\sin }^{2}x={\sin }^{2}x$

$-1-\sin x+6{\sin }^{2}x=0$

$(\sin x-\frac{1}{2})(\sin x+\frac{1}{3})=0$

$\sin x-\frac{1}{2}=0\Rightarrow x=\frac{\pi }{6}$

$\sin x+\frac{1}{3}=0\Rightarrow x=\frac{5\pi }{6}$