Question

How do you find the value of `cos105` without using a calculator?

Answer 1

`cos105` = `(1-sqrt3)/(2sqrt2)`

Explanation:

You can write `cos(105)` as `cos(45+60)`
Now, `cos(A+B)=cosAcosB-sinAsinB`

So, `cos(105)=cos45cos60-sin45sin60`

=`(1/sqrt2)*(1/2)-(1/sqrt2)((sqrt3)/2)`

=`(1-sqrt3)/(2sqrt2)`