Question

show that cos165 + sin165 = cos135​

Answer 1

cos165° + sin165°
= cos165° + sin(90° - 75°)
= cos165° + cos75°
= 2cos(165° + 75°)/2 * cos(165° - 75°)/2
= 2cos120° cos45°
= 2cos(180° - 60°) * cos(180° - 135°)
= 2 * [- cos60°] * [- cos135°]
= 2 * (-1/2) * (-135°)
= cos135°