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If A + B + C = 180^(@), then what is sin...

If `A + B + C = 180^(@)`, then what is sin 2A - sin 2N - sin 2C equal to ?

A

`-4 sin A sin B sin C`

B

`-4 cos A sin B cos C`

C

`-4 cos A cos B sin C`

D

`-4 sin A cos B cos C`

Text Solution

Verified by Experts

The correct Answer is:
D
`sin 2A - sin 2B - sin 2C`
`=2cos(A+B).sin(A-B)+sin(2A + 2B)`
`=2cos(A+B)sin(A-B)+2sin(A+B)cos(A+B)`
`=2cos(A+B)[sin(A-B)+sin(A+B)]`
`=-4sin A cos B cos C`
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