Find the Value of Cos 15 Degrees ?

Solution :

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

Proof :

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

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

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

$\implies$ cos 15 = $1\over \sqrt{2}$ $\times$ $\sqrt{3}\over 2$ + $1\over \sqrt{2}$ $\times$ $1\over 2$

$\implies$ cos 15 = $\sqrt{3} + 1\over 2\sqrt{2}$