Question

Find the exact value using a sum or difference identity of cos 105°

Answer 1

Explanation:

We can easily determine the exact value of this unknown angle by breaking it into known angles that can add together to give up 105. For example, 105 degrees is 60 + 45, both of which are found on the unit circle. We ill also use the trig identity for the sum of the cos of 2 angles which is:

`cos(60+45)=cos60cos45-sin60sin45`

These values are found on the units circle, so make sure you have one handy. Those values fill in as follows:

`((1)/(2))((√(2) )/(2))-((√(3) )/(2))((√(2) )/(2))` which simplifies to

`(√(2)-√(6) )/(4)`