Question

Please help! Find the exact value for cos 165° using the half-angle identity. I have gotten to cos82.5°=+-sqrt(1-.96)/2
The answer I got was cos82.5°=.366
Can someone double check my work?

Answer 1

cos 165
= -cos 15
= -cos (30/2)
= -sqrt [(1+cos30)/2]
= -sqrt [(1+sqrt(3)/2)/2]
= -sqrt [2+sqrt(3)]/2
Do you see how I did it?

Answer 2

\[-\sqrt{2+\sqrt{3}}/2\]

Answer 3

/2 is outside the sqrt

Answer 4

-.97 is the answer based on my work/solution!