Step-by-step explanation:
cos330° = cos(360° - 30°) = cos(2π - 30°)
Using, cos(2π - x) = cosx, x < 90°
=> cos(2π - 30°)
=> cos(30°)
=> √3/2 , proved
(ii): tan(165°) = tan(180° - 15°) = tan(π - 15°)
Using, tan(π - x) = - tanx
=> tan(π - 15°)
=> - tan15°
=> - (-√3 + 2)
=> √3 - 2 proved
For tan15° :
Using, tan2x = 2tanx/(1 - tan²x)
tan30° = 2tan15°/(1 - tan²15°)
1/√3 = 2tan15° / (1 - tan²15°)
1 - a² = 2√3 a {a = tan15°}
Solving this we get, a = -√3±2
As a = tan15°, it can't be -ve, thus
a = tan15° = -√3 + 2
