Question

Cos2x=cos60.cos30+sin60.sin30 find sin2x

Answer 1

Question : cos2x = cos60.cos30+sin60.sin30 , Find sin2x

Answer : 1/2

Step by step explanation :

We know that :

cos 60° = 1/2

cos 30° = √3/2

sin 60° = √3/2

sin 30° = 1/2

Now, Substitute these values :

= (1/2) × (√3/2) + (√3/2) × (1/2)

= (√3/4) + (√3/4)

cos 2x = (√3/2)

We know that,

sin A = √(1 - cos^2 A)

sin 2x = √(1 - (√3/2)^2)

sin 2x = √(1 - 3/4)

sin 2x = √(4- 3/4)

sin 2x = √(1/4)

sin 2x = 1/2

Hence,

Value of sin 2x = 1/2

Answer 2

$<b>We know that</b>$

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

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

$\huge\mathfrak{Answer}$

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