Question

If $sin\theta =sin15^{\circ }+sin45^{\circ }$, where $0^{\circ }<\theta <180^{\circ }$, then $\theta$ is equal to

• A. $45^{\circ }$
• B. $150^{\circ }$
• C. $60^{\circ }$
• D. $75^{\circ }$

Answer 1

Answer: (D)

We have, $sin\theta =sin15^{\circ }+sin45^{\circ }$
$sin\theta =2sin{\left(\frac{15+45}{2}\right)}^{\circ }cos{\left(\frac{15-45}{2}\right)}^{\circ }$
$=2sin30^{\circ }cos15^{\circ }$
$=2\times \frac{1}{2}cos15^{\circ }=cos15^{\circ }$
$\Rightarrow sin\theta =sin{\left(90-15\right)}^{\circ }$
$\Rightarrow \theta =75^{\circ }$