Question

If cos2x = cos60° × cos30° + sin60° × sin30°, find sin2x

Answer 1

Answer:

This is the answer of ur question

Answer 2

Answer:

$\text{The value of sin 2x is }\frac{1}{2}$

Step-by-step explanation:

Given

$\cos2x=\cos60\times \cos30+\sin60\times \sin 30$

we have to find the value of sin 2x.

To find the value of sin2x, first we will evaluate the right hand side of the above equality and then we will use the following formula from trigonometry.

$sinx=\sqrt{1-cos^2x}$

Now,

$\cos2x=\cos60\times \cos30+\sin60\times \sin 30\\\\=\frac{1}{2}\times \frac{\sqrt3}{2}+ \frac{\sqrt3}{2}\times \frac{1}{2}\\\\=\frac{\sqrt3}{4}+\frac{\sqrt3}{4}\\\\=\frac{\sqrt3}{2}$

$\sin2x=\sqrt{1-cos^22x}\\\\=\sqrt{1-(\frac{\sqrt3}{2})^2}\\\\=\sqrt{1-\frac{3}{4}}\\\\=\sqrt{\frac{1}{4}}=\frac{1}{2}$

$\text{The value of sin 2x is }\frac{1}{2}$