Prove: ${(sin A + cos A)}^{2} = 1 + sin 2 A$ .

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Solution

On LHS we have
$(sin A + cos A)^{2} = {sin}^{2} A + 2 sin A cos A + {cos}^{2} A$

$∵ {sin}^{2} A + {cos}^{2} A = 1$ , we get

$= 1 + 2 sin A cos A$

We know, $2 sin A cos A = sin 2 A$

$= 1 + sin 2 A$
Which is equal to RHS, hence proved.

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