Question

prove that sinA.sin(A+B) = sin^A.cosB+1/2 ×sin2A.sinB

Answer 1

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Answer 2

Hi ,

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1 ) sin( A + B ) = sinAcosB+cosA sinB

2 ) 2sinAcosA = sin2A

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Now ,

LHS = sinAsin( A+ B )

= sinA[ sinAcosB + cosAsinB ]

= sin² A cosB + sinAcosAsinB

= sin² A cosB + (1/2× 2sinAcosA)sinB

= sin² A cosB +(1/2) sin2AsinB

= sin² AcosB +( 1/2 )sin2A sinB

= RHS

Hence proved .

I hope this helps you.

: )