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Question

Mathematics Question on Trigonometric Functions

What is the value of sin⁡ 10∘+sin⁡ 50∘−sin⁡ 70∘\sin \, 10^{\circ} + \sin \, 50^{\circ} - \sin \, 70^{\circ} ?

A

1

B

0

C

12\frac{1}{2}

D

2

Answer

0

Explanation

Solution

The given expression sin⁡ 10∘+sin⁡ 50∘−sin⁡ 70∘\sin \, 10^{\circ} + \sin \, 50^{\circ} - \sin \, 70^{\circ} can also be written as sin⁡ 10∘−(sin⁡ 70∘−sin⁡ 50∘)\sin \, 10^{\circ} - (\sin \, 70^{\circ} - \sin \, 50^{\circ}) =sin⁡ 10∘−(2 cos⁡ 60∘ sin⁡ 10∘)= \sin \, 10^{\circ} - (2 \, \cos \, 60^{\circ} \, \sin \, 10^{\circ}) =sin⁡ 10∘(2 cos⁡ 60∘−1)=sin⁡ 10∘(1−1)=0= \sin \, 10^{\circ} (2 \, \cos \, 60^{\circ} - 1) = \sin \, 10^{\circ}( 1 - 1) = 0