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

-1

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Solution

The correct option is B
(b) Given, (cos x + sin x) $^{2}$ + k sin x cos x - 1 = 0, $\forall$ x
$\Rightarrow$ cos $^{2}$ x +sin $^{2}$ x + 2cos x sin x + k sin x cos x - 1 = 0, $\forall$ x
$\Rightarrow$ (k + 2)cos x sin x = 0, $\forall$ x
$\Rightarrow$ k = -2

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