# 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 = $$\sqrt{3} – 1\over 2\sqrt{2}$$