Cos 20° cos 40° cos 60° cos 80° =1/16 prove
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Step-by-step explanation:
cos20°.cos40°.cos60°.cos80° = 1/16
L.H.S.
=(cos20°.cos40°)cos60°.cos80°
=1/2[cos(20° + 40°) + cos(20° – 40°)]×1/2×cos80°
=1/4[cos60° + cos(-20°)]cos80°
=1/4[cos60°cos80° + cos20°cos80°]
=1/4[1/2cos80° + 1/2{cos(20° + 80°) + cos(20° – 80°)}]
=1/8[cos80° + {cos100° + cos(-60°)}]
=1/8[cos80° + cos100° + cos60°]
=1/8[cos80° +cos(180° – 80°) +cos60°]
=1/8[cos80° – cos80° + cos60°]
=1/8 ×cos60°
=1/8 × 1/2
=1/16 = R.H.S
L.H.S = R.H.S = 1/16 Hence proved
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