Prove that: Cos36Cos42Cos60Cos78=1/16
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Prove that: Cos36Cos42Cos60Cos78=1/16
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Answer:
L.H.S.=cos36cos42cos60cos78=1/16
=1/2[2cos42cos78] cos60cos36
=1/2[cos(42+78) +cos(42-78) ]×1/2×√5+1/4
=1/22[cos120+cos36]×√5+1/8
=1/2[cos(90+30) +cos36]×√5+1/8
=1/2[-sin30+cos36]×√5+1/8
=1/2[-1/2+√5+1/4]×√5+1/8
=1/2[-2+√5+1/4]√5+1/8
=1/2[√5-1/4]√5+1/8
=1/2×√5-1/4×1/2×√5-1/4
=1/2×1/2×(√5-1/4) ×(√5+1/4)
=1/4×5-1/16
=1/4×4/16
=1/16
L.H.S.=R.H.S.
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