Question

Solve : $4\sin x\cos x+2\sin x+2\cos x+1=0$

• A. $x={120}^0$
• B. $x={220}^0$
• C. $x={110}^0$
• D. $x={270}^0$

Answer 1

The correct option is A $x={120}^0$

$4\sin x\cos x+2\sin x+2\cos x+1=0$

$⟹2\sin x(2\cos x+1)+1(2\cos x+1)=0$

$⟹(2\sin x+1)(2\cos x+1)=0$

$⟹2\sin x+1=0$ (or) $2\cos x+1=0$

$⟹\sin x=\frac{-1}{2}$ (or) $\cos x=\frac{-1}{2}$

$⟹x={210}^{\circ },{330}^{\circ }$ (or) $x={120}^{\circ },{240}^{\circ }$

$x={120}^{\circ }$ is satisfy the given equation

Option A is correct