If $(sin x + cos x = a)$ , then $1 + 2 sin x cos x = a^{2}$

True

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False

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Solution

The correct option is A True
We are given $sin x + cos x = a$ .
We have to check if $1 + 2 sin x cos x = a^{2}$ .
For that,

$(sin x + cos x)^{2}$ = $a^{2}$

${sin}^{2} x + {cos}^{2} x + 2 sin x cos x$ = $a^{2}$

$1 + 2 sin x cos x$ = $a^{2}$

Hence, if $(sin x + cos x = a)$ , then $1 + 2 sin x cos x = a^{2}$

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