If $sin A + cos A = 1$ , then $sin 2 A$ is equal to.

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Solution

The correct option is B $0$
$sin A + cos A = 1$
$∴ (sin A + cos A)^{2} = 1^{2}$
$∴ {sin}^{2} A + {cos}^{2} A + 2 sin A cos A = 1$
$∴ 1 + sin 2 A = 1$
$∴ sin 2 A = 0$

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Similar questions

sin A + cos A = 1

sin 2 A =

\frac{s i n A + c o s A}{s i n A - c o s A} + \frac{s i n A - c o s A}{s i n A + c o s A} = \frac{2}{s i n^{2} A - c o s^{2} A} = \frac{2}{2 s i n^{2} A - 1} = \frac{2}{1 - 2 c o s^{2} A}

sin 2 A = \frac{1}{2}

sin 2 B = - \frac{1}{2}

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