Answer :

LHS


= sin 600° cos 390° + cos 480° sin 150°


= sin (90° × 6 + 60°) cos (90° × 4 + 30°) + cos (90° × 5 + 30°) sin (90° × 1 + 60°)


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


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


= -sin 60° cos 30° - sin 30° cos 60°


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


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


= -sin (60° + 30°)


= -sin 90°


= -1


= RHS


Hence proved.


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