Question

If $\cos 2\theta =2{\cos }^2\theta -1$, then value of $\cos {60}^o$ is :

• A. $1$
• B. $\frac{1}{2}$
• C. $0$
• D. $2$

Answer 1

Answer: (B)

$\frac{1}{2}$

Put $\theta ={30}^o\cos 2\left({30}^o\right)=2{\cos }^2{30}^o-1$
$\therefore {2\left(\frac{\sqrt{3}}{2}\right)}^2-1=2\times \frac{3}{4}-1$
$=\frac{3}{2}-1=\frac{3-2}{2}=\frac{1}{2}$
$\therefore \cos {60}^o=\frac{1}{2}$