Answer:

Explanation:
Find the exact value of cos(105°).
The method I am about to show you will allow you to complete this problem without a calculator. Although, memorizing the trigonometric identities and the unit circle is required.
We have,

Using the angle sum identity for cosine.

Split the given angle, in degrees, into two angles. Preferably two angles we can recognize on the unit circle.

Now applying the identity.

Now utilizing the unit circle.


Now simplifying...
