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

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(B) Given the equation is an identity,it must hold true for all values of $x$.Expanding the expression: $(\cos^2 x + \sin^2 x) + 2 \sin x \cos x + k \

Vedclass · Accepted Answer

$-2$

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(B) Given the equation is an identity,it must hold true for all values of $x$.Expanding the expression: $(\cos^2 x + \sin^2 x) + 2 \sin x \cos x + k \sin x \cos x - 1 = 0$.Using the trigonometric identity $\cos^2 x + \sin^2 x = 1$,we substitute it into the equation:$1 + 2 \sin x \cos x + k \sin x \cos x - 1 = 0$.Simplifying the equation:$(2 + k) \sin x \cos x = 0$.For this to be an identity (true for all $x$),the coefficient of $\sin x \cos x$ must be zero.Therefore,$2 + k = 0$,which gives $k = -2$.

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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