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The value of sin 10^(@) sin 30^(@) sin ...

The value of `sin 10^(@) sin 30^(@) sin 50^(@) sin 70^(@)` is equal to .

A

`(1)/(36)`

B

`(1)/(32)`

C

`(1)/(16)`

D

`(1)/(18)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have, sin `10^(@) sin 50^(@) sin 70^(@)`
`=sin (30^(@))[sin(10^(@))sin(50^(@))sin (70^(@))]`
`=(1)/(2)[sin(10^(@))sin(60^(@)-10^(@))sin(60^(@)+10^(@))]`
`=(1)/(2)[(1)/(4)sin(3(10^(@)))] " "[because sin theta sin (60^(@)-theta)sin(60^(@)+theta)=(1)/(4)sin3 theta]`
`=(1)/(8)sin 30^(@) = (1)/(8) xx (1)/(2) = (1)/(16)`
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