Question

Find the value of sin 2 60 - sin 2 30

Answer 1

Sin^2 60-sin^2 30 = (√3/2)^2-(1/2)^2 = 3/4-1/4 = 2/4=1/2

Answer 2

Given,

An expression.

To find,

The value of $\sin^2 60 - \sin^2 30$

Solution,

We know that,

$\sin 60=\dfrac{\sqrt 3}{2}\\\\\sin 30=\dfrac{1}{2}$

The expression becomes,

$\sin^2 60 - \sin^2 30=(\dfrac{\sqrt 3}{2})^2-(\dfrac{1}{2})^2\\\\=\dfrac{3}{4}-\dfrac{1}{4}\\\\=\dfrac{2}{4}\\\\=\dfrac{1}{2}$

So, the value of $\sin^2 60 - \sin^2 30$ is 1/2.