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If the area of a DeltaABC be lambda, the...

If the area of a `DeltaABC` be `lambda`, then `a^(2)sin2B+b^(2)sin2A` is equal to

A

`2lambda`

B

`lambda`

C

`4lambda`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`a^(2)sin2B+b^(2)sin2A`
`=2a^(2)sinB.cosB+2b^(2)sinAcosA`
`=(a^(2)b)/(R)cosB+(b^(2)a)/(R)cosA`
`=(ab)/(R)(acosB+bcosA)=(abc)/(R)=2bcsinA`
`=4((1)/(2)bcsinA)=4lambda`
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