Question

The value of `cos 65^(@)cos 55^(@)cos5^(@)` is
A. `(sqrt(3)+1)/(8sqrt(2))`
B. `(sqrt(3)-1)/(8sqrt(2))`
C. `(sqrt(3)+1)/(4sqrt(2))`
D. `(sqrt(3)-1)/(4sqrt(2))`

Answer 1

Correct Answer - A
`cos 65^(@)cos 55^(@)cos 5^(@)`
`=((cos 60^(@)+cos 50^(@))/(2)).cos 65^(@)`
`=(cos 65^(@))/(4)+(2cos50^(@)cos 65^(@))/(4)`
`= (cos cos 65^(@))/(4)+(cos 115^(@)+cos 15^(@))/(4)`
`=(2cos 90^(@)cos 25^(@)+cos 15^(@))/(4)`
`=(cos 15^(@))/(4)=(sqrt(3)+1)/(8sqrt(2))`