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If A+B+C=pi/2,prove that: sin2A-sin2B+...

If A+B+C=`pi/2`,prove that:
`sin2A-sin2B+sin2C=4sinAcosBsinC`

Text Solution

Verified by Experts

LHS`=sin2A-sin2B+sin2C`
`=2cos(A+B)sin(A-B)+2sinCcosC`
`=2cos(90^(@)-c)sin(A-B)+2sinCcos(90^(@)-(A+B)`
`=2sinC.sin(A-B)+2sinC.sin(A+B)`
`=2sin.2sinAcosB`
`=4sinAcosBsinC`
=RHS (Hence proved)
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