1. find the exact value of tan(15) using sum or difference identity
2. find the exact value of cos2x when sin(x) = 3/5 and pi/2 < x < pi.
1
tan (15) = sin/cos sin (45-30) = sin45 cos 30 - cos 45 sin30 =
cos(45-30) = cos45cos30 + sin 45 sin 30
sqrt2/2 sqrt3/2 - sqrt2/2 1/2 = sqrt2/2 (sqrt3/2-1/2) = 1/2 (sqrt3-1) = sqrt3-1
sqrt2/2 sqrt3/2 + sqrt2/2 1/2 sqrt2/2 (sqrt3/2 + 1/2) 1/2 (sqrt3+1) sqrt3+1
Multiply num and denom by (sqrt3-1) to finally get tan(15) = (2- sqrt3)