Prove that sin2A is equal to 2sinAcosA

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Solution

To Prove: sin2A = 2 sinA cosA.

Proof:

We know that, sin(A + B) = sinA cosB + cosA sinB.

Now put B = A in the above equation,
we get,

sin(A + A) = sinA cosA + cosA sinA

=> sin2A = sinA cosA + sinA cosA

=> sin2A = 2sinA cosA.

Hence proved that,

sin2A = 2sinA cosA.

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