Question

The general solution of $si{n}^{2}x-2cosx+\frac{1}{4}=0isx=\left(nϵZ\right)$

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$si{n}^{2}x-2cosx+\frac{1}{4}=0\Rightarrow 4(1-co{s}^{2}x)-8cosx+1=0\Rightarrow 4co{s}^{2}x+8cosx-5=0\Rightarrow 4co{s}^{2}x+10cosx-2cosx-5=0\Rightarrow (2cosx+5)(2cosx-1)=0\Rightarrow cosx=\frac{1}{2}=cos\frac{\pi }{3}\Rightarrow x=2n\pi \pm \frac{\pi }{3}.$