Find the Value of Sin 15 Degrees ?

Solution :

The value of sin 15 degrees is $\sqrt{3} – 1\over 2\sqrt{2}$.

Proof :

We will write sin 15 as sin (45 – 30).

By using formula sin (A – B) = sin A cos B – cos A sin B,

sin (45 – 30) = sin 45 cos 30 – cos 45 sin 30

$\implies$ sin 15 = $1\over \sqrt{2}$ $\times$ $\sqrt{3}\over 2$ – $1\over \sqrt{2}$ $\times$ $1\over 2$

$\implies$ sin 15 = $\sqrt{3} – 1\over 2\sqrt{2}$