Sin left( {frac{π }{{10}}} right)sin left( {frac{{3π }}{{10}}} right) =

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3.Trigonometrical Ratios, Functions and Identities

easy

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

A

$1/2$

B

$-1/2$

C

$1/4$

D

$1$

Solution

(c) $\sin \frac{\pi }{{10}}\sin \frac{{3\pi }}{{10}} = \sin 18^\circ .\sin 54^\circ $

$ = \sin 18^\circ .\cos 36^\circ = \frac{{\sqrt 5 – 1}}{4}.\frac{{\sqrt 5 + 1}}{4} = \frac{1}{4}$.

Standard 11

Mathematics

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