Question

If $\sin 7\theta =\cos 2\theta$ for acute angles $7\theta$ and $2\theta$, then $\theta =$

• A. $10$
• B. $90$
• C. $20$
• D. $30$

Answer 1

The correct option is A $10$

Given : $\sin 7\theta =\cos 2\theta$
$⟹\sin 7\theta =\sin ({90}^o-2\theta )$
$⟹7\theta ={90}^o-2\theta$
$⟹9\theta ={90}^o$
$⟹\theta ={10}^o$

Hence, the answer is ${10}^o$.