# How do you use the sum and difference identities to find the exact value of cos 75?

##### 1 Answer

The sum and difference identities are given as follows:

sum:

difference:

If you have an angle whose trig values you don't know, but that can be made by two angles you do know, you will use one of these identities.

Using our sum identity, where

Now just find these values on your unit circle and you get;

and the rest is arithmetic.

To use the difference identity, I would recommend using the angles;

Then, using difference identity;

Which gives;

Both expressions simplify to;