# What is the Formula of Cos(A + B) ?

In this post you will learn what is the formula for cos (A + B) with examples.

## Cos (A + B) Formula :

The formula of cos(A + B) is cos A cos B – sin A sin B.

Example : If sin A = $$3\over 5$$ and cos B = $$9\over 41$$, find the value of cos (A + B).

Solution : We have,

sin A = $$3\over 5$$ and cos B = $$9\over 41$$

$$\therefore$$  cos A = $$\sqrt{1 – sin^2 A}$$  and  sin B = $$\sqrt{1 – cos^2 B}$$

$$\implies$$  cos A = $$\sqrt{1 – {9\over 25}}$$ = $$4\over 5$$  and  sin B = $$\sqrt{1 – {81\over 1681}}$$ = $$40\over 41$$

Now, By using above formula,

cos (A + B) = cos A cos B – sin A sin B

= $$4\over 5$$ $$\times$$ $$9\over 41$$ – $$3\over 5$$ $$\times$$ $$40\over 41$$ = $$-84\over 205$$

Example : Find the value of cos 75.

Solution : cos 75 = cos (45 + 30)

By using above formula,

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 = $$\sqrt{3} – 1\over 2\sqrt{2}$$