Question

Prove that,

2cosAsinB=sin(A+B)-sin(A-B)

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Answer 1

Hello!

To Prove:

2cosA•sinA = sin(A+B)-sin(A-B)

Proof:

LHS = 2cosA • sinB

RHS

= sin(A+B)-sin(A-B)

= sinA•cosB+cosA•sinB -(sinA•cosB-cosA•sinB)

= sinA•cos+cosA•sinB -sinA•cosB+cosA•sinB

= 2cosA•sinB

Here,

LHS = RHS

Hence proved

______________________________

Identities used:

sin(A+B) = sinA•cosB+cosA•sinB

sin(A-B) = sinA•cosB-cosA•sinB

Answer 2

Answer:

2codAsinB=sin(A+B)-sin(A-B)

sinAcosB+cosAsinB-(sinAcosB-cosAsinB)

sinAcosB+cosAsinB-sinAcosB+cosAsinB

=2cosAsinB

hope it helps