Question

If $sin3\theta =\cos (\theta -6^{\circ }),$ where $3\theta$ and $\theta -6^{\circ }$ are acute angles, find the value of $\theta$

• A. $\theta ={24}^{\circ }$
• B. $\theta ={48}^{\circ }$
• C. $\theta ={14}^{\circ }$
• D. none of the above

Answer 1

The correct option is A $\theta ={24}^{\circ }$

$\sin 3\theta =\cos (\theta -6^{\circ })$
$\Rightarrow \cos ({90}^{\circ }-3\theta )=\cos (\theta -6^{\circ })$
$\Rightarrow 90-3\theta =\theta -6^{\circ }\Rightarrow 4\theta ={96}^{\circ }\Rightarrow \theta ={24}^{\circ }$