If $sin x + cos x = a,$ then $1 + 2 sin x cos x =$

a^{3}

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2 a

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a^{2}

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\frac{1}{a}

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Solution

The correct option is C $a^{2}$
We are given $sin x + cos x = a .$

Squaring both the sides, we get
$(sin x + cos x)^{2} = a^{2}$
$\Rightarrow {sin}^{2} x + {cos}^{2} x + 2 sin x cos x = a^{2}$
$∵ {sin}^{2} x + {cos}^{2} x = 1$
We get,
$1 + 2 sin x cos x = a^{2}$

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