prove that :

LHS

= sin 480° cos 690° + cos 780° sin 1050°

= sin (90° × 5 + 30°) cos (90° × 7 + 60°) + cos (90° × 8 + 60°) sin (90° × 11 + 60°)

We know that when n is odd, sin → cos and cos → sin.

= cos 30° sin 60° + cos 60° [-cos 60°]

= 3/4 - 1/4

= 2/4

= 1/2

= RHS

Hence proved.