Answer :

LHS


= sin 780° sin 480° + cos 120° sin 150°


= sin (90° × 8 + 60°) sin (90° × 5 + 30°) + cos (90° × 1 + 30°) sin (90° × 1 + 60°)


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


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


= sin 60° cos 30° - sin 30° cos 60°


We know that sin A cos B – cos A sin B = sin (A – B)


= sin (60° - 30°)


= sin 30°


= 1/2


= RHS


Hence proved.


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