Question

If $\sin$ $2\theta =\cos (\theta -6^{\circ })$ where $2\theta$ and $(\theta -6^{\circ })$ are both acute angles, then the value of $\theta$ is

• A. ${16}^{\circ }$
• B. ${32}^{\circ }$
• C. ${48}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

Answer: (B)

${32}^{\circ }$

Given:

$\sin 2\theta =\cos (\theta -6^{\circ })$

$\Rightarrow \cos (90-2\theta )=\cos (\theta -6^{\circ })$

$\Rightarrow (90-2\theta )=(\theta -6^{\circ })$

$\Rightarrow 3\theta ={96}^{\circ }$

$\Rightarrow \theta ={32}^{\circ }$