Answer :

LHS = cos 24° + cos 55° + cos 125° + cos 204° + cos 300°


= cos 24° + cos (90° × 1 – 35°) + cos (90° × 1 + 35°) + cos (90° × 2 + 24°) + cos (90° × 3 + 30°)


We know that when n is odd, cos sin.


= cos 24° + sin 35° - sin 35° - cos 24° + sin 30°


= 0 + 0 + 1/2


= 1/2


= RHS


Hence proved.


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