Question

If Cos2x=Cos60°•Cos30°+Sin60°•Sin30°,Find the value of Sin2x

Answer 1

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Answer 2

We know that

$\: \cos( \alpha - \beta ) = \cos( \alpha )\cos( \beta ) + \sin( \alpha )\sin( \beta )$

Here, we have

cos(2x) = cos(60°)cos(30°)+ sin(60°)sin(30°)

$\implies \: \cos(2x) = \cos(60 - 30)$

$\implies \: \cos(2x) = \cos(30) \\ \\ \implies \: 2x = 30 \\ \\ \implies \: x = 15 {}^{ \circ}$

Hence, sin(2x) = sin(30°)

We know that sin(30°) = 1/2

Hence, sin(2x) = 1/2

$\huge\mathfrak{Answer}$

$\sf \sin (2x) = \frac{1}{2}$