Question

If $\sin 3\theta =\cos (\theta -2^{\circ })where3\theta and(\theta -2^{\circ })$ are acute angles what is the value of $\theta$?

• A. ${22}^{\circ }$
• B. ${23}^{\circ }$
• C. ${24}^{\circ }$
• D. ${25}^{\circ }$

Answer 1

The correct option is B ${23}^{\circ }$

$\sin 3\theta =\cos (\theta -2°)$

$\Rightarrow \cos (90°-3\theta )=\cos (\theta -2°)$

$\Rightarrow 90°-3\theta =\theta -2$

$\Rightarrow 4\theta =92$

$\Rightarrow \theta =23°$

Hence, the answer is $23°.$