Question

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

Answer 1

Answer:

Step-by-step 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:

$(\frac{1}{2})(\frac{\sqrt{2} }{2})-(\frac{\sqrt{3} }{2})(\frac{\sqrt{2} }{2})$ which simplifies to

$\frac{\sqrt{2}-\sqrt{6} }{4}$