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

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Question

(b) Given, ${(\cos x + \sin x)^2} + k\sin x\cos x - 1 = 0,\,\forall \,x$

==> ${\cos ^2}x + {\sin ^2}x + 2\cos x\sin x + k\sin x\cos x - 1 = 0,\,

Vedclass · Accepted Answer

$-2$

Vedclass · Answer

(b) Given, ${(\cos x + \sin x)^2} + k\sin x\cos x - 1 = 0,\,\forall \,x$

==> ${\cos ^2}x + {\sin ^2}x + 2\cos x\sin x + k\sin x\cos x - 1 = 0,\,\forall \,x$

==> $(k + 2)\cos x\sin x = 0,\,\forall \,x$ ==> $k + 2 = 0$ ==> $k = - 2$.

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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