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Question: \[\sin\left( \frac{\pi}{10} \right)\sin\left( \frac{3\pi}{10} \right) =\]...

sin⁡(π10)sin⁡(3π10)=\sin\left( \frac{\pi}{10} \right)\sin\left( \frac{3\pi}{10} \right) =

A

1/2

B

– 1/2

C

1/4

D

1

Answer

1/4

Explanation

Solution

sin⁡π10sin⁡3π10=sin⁡18∘.sin⁡54∘\sin\frac{\pi}{10}\sin\frac{3\pi}{10} = \sin 18{^\circ}.\sin 54{^\circ}

=sin⁡18∘.cos⁡36∘=5−14.5+14=14= \sin 18{^\circ}.\cos 36{^\circ} = \frac{\sqrt{5} - 1}{4}.\frac{\sqrt{5} + 1}{4} = \frac{1}{4}.