Find the exact value of cos(15◦ ) − cos(75◦ ). Do not use calculator. Use trigonometric identities.

Answer 1

There are a few potential identities you could use. To find cos(15°), you can use a half angle identity or a difference identity. The same is true for cos(75°). The difference sin(15°) - cos(75°) is probably most easily found with the sum to product identity:

cos(a) - cos(b) = -2sin((a+b)/2)sin((a-b)/2),

so cos(15°) - cos(75°) = -2sin(45°)sin(-30°) = -2(sqrt(2)/2)(-1/2) = sqrt(2)/2.