Question

If $\cos 2\theta =-\frac{1}{2}$, value of $\cos \theta$ is

• A. $\pm \frac{1}{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{\sqrt{3}}{2}$
• D. $1$

Answer 1

Answer: (A)

$\pm \frac{1}{2}$

$cos2\theta =\frac{-1}{2}$

we know $co{s}^2\theta =2co{s}^2-1$

$2co{s}^2\theta =1-\frac{1}{2}=\frac{1}{2}.$

$co{s}^2=\frac{1}{4}$

$cos\theta =\sqrt{\frac{1}{4}}$ =$\frac{+1}{2}$

$\therefore$ $cos\theta =\pm \frac{1}{2}$