Find the Value of Cos 75 Degrees ?

Solution :

The value of cos 75 degrees is $\sqrt{3} – 1\over 2\sqrt{2}$.

Proof :

We will write cos 75 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 75 = $1\over \sqrt{2}$ $\times$ $\sqrt{3}\over 2$ – $1\over \sqrt{2}$ $\times$ $1\over 2$

$\implies$ cos 75 = $\sqrt{3} – 1\over 2\sqrt{2}$