Question

prove that cos20cos40cos60cos80=1/6
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Answer 1

Ans0

Step-by-step explanation:

cos20cos40cos60cos80=1/6  

multipling both sides by 0\

0*cos20cos40cos60cos80=1/6  *0

0=0

hence proved

xD

Answer 2

Answer:

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

since

cos(-A)=cosA

cosA.cosB=1/2[cos(A + B) + cos(A – B)]

cos60°=1/2