Question -
Answer -
Let us consider LHS:
cos 78o cos 42o cos 36o
Let us multiply and divide by 2 we get,
cos 78o cos 42o cos 36o =1/2 (2 cos 78o cos 42o cos 36o)
We know, 2 cos A cos B = cos (A + B) + cos (A – B)
Then the above equation becomes,
= 1/2 (cos (78o + 42o) +cos (78o – 42o)) × cos 36o
= 1/2 (cos 120o + cos 36o)× cos 36o
= 1/2 (cos (180o – 60o) +cos 36o) × cos 36o
= 1/2 (-cos (60o) + cos 36o) ×cos 36o [since, cos(180° – A) = – A]
= 1/2 (-1/2 + (√5 + 1)/4) ((√5 + 1)/4) [since, cos 36o =(√5 + 1)/4]
= 1/2 (√5 + 1 – 2)/4 ((√5 + 1)/4)
= 1/2 (√5 – 1)/4) ((√5 + 1)/4)
= 1/2 ((√5)2 – 12)/16
= 1/2 (5-1)/16
= 1/2 (4/16)
= 1/8
= RHS
Hence proved.