Prove that: cos 7π/12 + cos π/12 = sin 5π/12 – sin π/12

Question

Philoid · Accepted Answer

⇒ 7π/12 = 105°, π/12 = 15°; 5π/12 = 75°

LHS = cos 105° + cos 15°

= cos(90° + 15°) + sin(90° - 75°)

= -sin 15° + sin 75°

= sin 75° - sin 15° = RHS

Hence proved.