The value of sin `10^(@)` sin `30^(@)` sin `50^(@)` sin `70^(@)` is
A. `(1)/(36)`
B. `(1)/(32)`
C. `(1)/(16)`
D. `(1)/(18)`
A. `(1)/(36)`
B. `(1)/(32)`
C. `(1)/(16)`
D. `(1)/(18)`
Correct Answer – 4
The value of sin `10^(@)` sin `30^(@)` sin `50^(@)` sin `70^(@)` is
The value of sin 10.sin 30. sin 50.sin 70 is
A. `1/36`
B. `1/32`
C. `1/18`
D. `1/16`
The value of sin 10.sin 30. sin 50.sin 70 is
A. `1/36`
B. `1/32`
C. `1/18`
D. `1/16`
A. `1/36`
B. `1/32`
C. `1/18`
D. `1/16`
Correct Answer – 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)`