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In any triangle A B C ,sin^2A-sin^2B+sin...

In any triangle `A B C ,sin^2A-sin^2B+sin^2C` is always equal to `2sinAsinBcosC` (b) `2sinAcosBsinC` `2sinAcosBcosC` (d) `2sinAsinBsinC`

A

`2sin A sin B cosC`

B

`2 sin A cos B sinC`

C

`2 sin A cos B cos C`

D

`2 sin A sin B sinC`

Text Solution

Verified by Experts

The correct Answer is:
B
`sin^(2)A-sin^(2)sin^(2)C`
`=sin(A+B)sin(A-B)+sin^(2)C`
`=sinC(sin(A-B)+sinC)`
`=sinC(sin(A-B)+sin(A+B))`
`=2sin A cos B sin C`.
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