Question

Prove that: cos 20° cos 40° cos 60° cos 80° =1/16​

Answer 1

SOLUTION:-

Take L.H.S

cos20°.cos40°.cos60°.cos80°

➢(cos20°.cos40°)cos60°.cos80°

➢1/2[cos20°+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 [cos60° = 1/2]

➢1/16 = R.H.S

Therefore,

L.H.S = R.H.S = 1/16

Proved.

Hope it helps ☺️