Find the value of $k$ for which $(cos x + sin x)^{2} + k sin x cos x - 1 = 0$ is an identity.

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Solution

The correct option is B $- 2$
If identity it should holds for all $x$ .
so we put $x = \frac{π}{4}$
We get
$(\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}})^{2} + k \cdot \frac{1}{\sqrt{2}} \cdot \frac{1}{\sqrt{2}} - 1 = 0$
and get $k = - 2$

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