Answer :

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.


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