Question

COS20.COS40.COS60=1/8

Answer 1

Mate think that there is a Problem in your Ques. :-

(There is cos 80 not cos 60)

If there is cos 80.

See the Answer Below Mate :-

#Solution :-

L.H.S. = cos 20.cos 40.cos 80

= cos 80.cos 20.cos 40

= 1/2 (2 cos 80.cos 20). cos 40

= 1/2 (cos 100 + cos 60). cos 40

= (1/2 cos 100.cos 40)+(1/2 cos 60.cos 40)

= [1/2 {1/2(2cos 100.cos 40)}] + 1/2 × 1/2 cos 40

= 1/4 (cos 140 + cos 60) + 1/4 cos 40

= 1/4 cos 140 + 1/4 cos 60 + 1/4 cos 40

= 1/4 cos 140 + 1/4 cos 40 + 1/4 cos 60

= 1/4 (cos 140 + cos 40 ) + 1/4 cos 60

= 1/4 [cos (100 - 40) + cos 40] + 1/4 × 1/2

= 1/4 ( - cos 40 + cos 40) + 1/8

= 1/4 × 0 + 1/8

= 0 + 1/8

= 1/8

= R.H.S