Question

The least difference between the roots of the equation $4cosx(2-3si{n}^{2}x)+(cos2x+1)=0(0\le x\le \frac{\pi }{2})$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

The given equation can be written as $4cosx(3co{s}^{2}x–1)+2co{s}^{2}x=0$
$\Rightarrow 2cosx(6cos2x+cosx–2)=0\Rightarrow 2cosx(3cosx+2)(2cosx–1)=0$
$\Rightarrow$ either cos x = 0 which gives $x=\frac{\pi }{2}$
or $cosx=–\frac{2}{3}$, which gives no value of x for which 0 $\le x\le \frac{\pi }{2}$
or $cosx=\frac{1}{2}$, which gives $x=\frac{\pi }{3}$
So the required difference $=\frac{\pi }{2}-\frac{\pi }{3}=\frac{\pi }{6}$