evaluate without using a calculator, leaving your answer as surds

Question

(a)sin105 degrees
(b)tan15 degrees
(c)cos 75 degrees

Answer 1

sin 15 = sin 30/2
= √[(1-cos 30)/2]
= 1/2 √(2-√3)
cos 15 = 1/2 √(2+√3)

sin 105 = sin(90+15) = sin 90 cos 15 - cos 90 sin 15 = 1/2 √(2-√3)

tan 15 = √(2-√3)/√(2+√3) = 2-√3 = 1/(2+√3)

cos 75 = cos(90-15) = cos90cos15 + sin90 sin15 = 1/2 √(2-√3)

Answer 2

Oops: sin 105 = cos 15