Prove cos 27 + cos 93 + cos 147 = 0
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cos27°+cos93°+cos147°
=2cos(27°+93°)/2cos(27°-93°)/2+cos147°
=2cos60°cos33°+cos(180°-33°)
=2×1/2cos33°+cos{(90°×2)-33°} [∵, cos60°=1/2 and cos(180°-Ф)=-cosФ]
=cos33°+(-cos33°)
=cos33°-cos33°
=0 (Proved)
=2cos(27°+93°)/2cos(27°-93°)/2+cos147°
=2cos60°cos33°+cos(180°-33°)
=2×1/2cos33°+cos{(90°×2)-33°} [∵, cos60°=1/2 and cos(180°-Ф)=-cosФ]
=cos33°+(-cos33°)
=cos33°-cos33°
=0 (Proved)
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