Solveeit Logo
Login

Question

Mathematics Question on Trigonometric Functions

If sin θ=sin 15∘+sin 45∘sin\, \theta = sin \,15^{\circ}+ sin\, 45^{\circ}, where 0∘<θ<180∘0^{\circ} < \theta < 180^{\circ}, then θ\theta is equal to

A

45∘45^{\circ}

B

150∘150^{\circ}

C

60∘60^{\circ}

D

75∘75^{\circ}

Answer

75∘75^{\circ}

Explanation

Solution

We have, sin θ=sin 15∘+sin 45∘sin\,\theta=sin\,15^{\circ}+sin\,45^{\circ} sin θ=2 sin(15+452)∘ cos(15−452)∘sin\,\theta=2\,sin\left(\frac{15+45}{2}\right)^{\circ}\,cos\left(\frac{15-45}{2}\right)^{\circ} =2 sin30∘ cos 15∘=2\,sin30^{\circ}\,cos\,15^{\circ} =2×12 cos 15∘=cos 15∘=2\times\frac{1}{2}\,cos\,15^{\circ}=cos\,15^{\circ} ⇒sin θ=sin(90−15)∘\Rightarrow sin\,\theta=sin\left(90-15\right)^{\circ} ⇒θ=75∘\Rightarrow \theta=75^{\circ}