Question

cos20 cos 40 cos 60 cos 30 =1/16​

Answer 1

Answer:

hii friend here is your answer

.

=(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