The value of k,for which (cos x + sin x)^2 + | vedclass

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(B) Given the equation: $(\cos x + \sin x)^2 + k \sin x \cos x - 1 = 0, \forall x$Expanding the square: $(\cos^2 x + \sin^2 x + 2 \sin x \cos x) + k \

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$-2$

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(B) Given the equation: $(\cos x + \sin x)^2 + k \sin x \cos x - 1 = 0, \forall x$Expanding the square: $(\cos^2 x + \sin^2 x + 2 \sin x \cos x) + k \sin x \cos x - 1 = 0, \forall x$Using the identity $\cos^2 x + \sin^2 x = 1$: $1 + 2 \sin x \cos x + k \sin x \cos x - 1 = 0, \forall x$Simplifying the equation: $(2 + k) \sin x \cos x = 0, \forall x$For this to be an identity (true for all $x$),the coefficient must be zero:$2 + k = 0$$k = -2$

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

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