Question

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

• A. -1
• B. -2
• C. 0
• D. 1

Answer 1

Answer: (B)

Given ${\left(\cos x+\sin x\right)}^2+k\sin x\cos x-1=0\forall x$
$\Rightarrow {\cos }^{2}x+{\sin }^{2}x+2\cos x\sin x+k\sin x\cos x-1=0\forall x$
$\Rightarrow \left(k+2\right)\cos x\sin x=0\forall x$
$\Rightarrow k+2=0\Rightarrow k=-2$