Question

If $\cos ({20}^{\circ }+\theta )=\sin {30}^{\circ }$, then the value of $\theta$ is :

• A. ${20}^{\circ }$
• B. ${50}^{\circ }$
• C. ${30}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is D ${40}^{\circ }$

$\cos (20°+\theta )=\sin 30°$

$\Rightarrow \cos (20°+\theta )=\cos (90°-30°)$

$\Rightarrow 20°+\theta =60°$

$\Rightarrow \theta =40°$

Hence, the answer is $40°.$