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The value of sin50^(@)-sin70^(@)+sin10^...

The value of `sin50^(@)-sin70^(@)+sin10^(@)` is

A

1

B

`(1)/(sqrt(2))`

C

`(sqrt(3))/(2)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
Consider `sin50^(@)-sin70^(@)+sin10^(@)`
`=2"cos "(70^(@)+50^(@))/(2)." sin "(50^(@)-70^(@))/ (2)+sin10^(@)`
`[becausesinA-sinB=2cos((A+B)/(2))sin((A-B)/(2))]`
`=-2cos60^(@)sin10^(@)+sin10^(@)=-sin10^(@)+sin10^(@)=0(becausecos60^(@)=(1)/(2))`
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