Question

If $\cos (12+\theta )=\frac{\sqrt{3}}{2}$; $0<\theta <{20}^{\circ }$, then the value of $\theta$ is

• A. ${45}^{\circ }$
• B. ${40}^{\circ }$
• C. ${18}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is C ${18}^{\circ }$

$\cos (12+\theta )=\frac{\sqrt{3}}{2}$

But $\cos {30}^{\circ }=\frac{\sqrt{3}}{2}$

$\therefore \cos (12+\theta )=\cos {30}^{\circ }$

$\therefore 12+\theta ={30}^{\circ }$
So, $\theta ={18}^{\circ }$

So, option $C$ is correct.