Question

prove that sin 50 degrees +sin 10 degres = cos20 degrees

Answer 1

Since sin A + sin B = 2 sin [(A + B)/2] cos [(A - B)/2]

So, sin 50° + sin 10° = 2 sin [(50° + 10°)/2] cos [(50° - 10°)/2]

= 2 sin (60°/2) cos (40°/2)

= 2 sin 30° cos 20°

= 2 × 1/2 × cos 20°

= cos 20°