Question

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

Answer 1

As we know that, 7π/12 = 105°, π/12 = 15°; 5π/12 = 75°

Let us consider the LHS: cos 105° + cos 15°

cos (90° + 15°) + sin (90° – 75°)

-sin 15° + sin 75°

sin 75° – sin 15°

= RHS

∴ LHS = RHS

Thus proved.