Question

7
(ii) cos 20° cos 40° cos 80°=1/8​

Answer 1

Answer:

cos 20° cos 40° cos 80°=1/8

Soln,

LHS

= cos 20° cos 40° cos 80°

= 2 cos 20°cos 40°/2 cos80°

= cos(20° + 40°) + cos( 20° - 40°) / 2cos80°

= cos 60° + cos (-20°) / 2 cos 80°

= 1/2 + cos 20° /2 cos 80°

= cos 80°/ 4 + cos 20°cos 80°/ 2

= cos 80°/ 4 + 2cos 20°cos 80°/ 4

=cos 80°/4 +cos(20+80°)+cos(20° - 80°)/4

= cos 80°/ 4 + cos100° + cos 60°/4

= cos 80°/ 4 + cos100° / 4 + 1/4 x 2

= cos 80° + cos100° / 4 + 1/8

= [2 cos (80°+100°) /2cos(80°-100° )/2 ] / 4 + 1/8

= 2 cos 90° cos(-20) / 4 + 1/8

= 2 x 0 x cos(-20) / 4 + 1/8

= 0 / 4 + 1/8

= 0 + 1/8

= 1/8 = R.H.S

## proved