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The value of cos 65^(@)cos 55^(@)cos5^(@...

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))`

Text Solution

Verified by Experts

The correct Answer is:
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))`
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