The value of $k$ for which $(cos x + sin x)^{2} + k sin x cos x - 1 = 0$ is that identity, is.

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Solution

The correct option is B $- 2$
Given : $(cos x + sin x)^{2} + k sin x cos x - 1 = 0$
$⟹ {cos}^{2} x + {sin}^{2} x + 2 sin x cos x + k sin x cos x - 1 = 0$
$⟹ 1 + 2 sin x cos x + k sin x cos x - 1 = 0$
$⟹ (2 + k) sin x cos x = 0$
$⟹ 2 + k = 0$ ...... $[∵ sin x cos x \neq 0]$
$⟹ k = - 2$
Hence, option B is correct.

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