- Home
- Standard 11
- Mathematics
3.Trigonometrical Ratios, Functions and Identities
medium
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
$1$
Solution
(b) Given, ${(\cos x + \sin x)^2} + k\sin x\cos x – 1 = 0,\,\forall \,x$
==> ${\cos ^2}x + {\sin ^2}x + 2\cos x\sin x + k\sin x\cos x – 1 = 0,\,\forall \,x$
==> $(k + 2)\cos x\sin x = 0,\,\forall \,x$ ==> $k + 2 = 0$ ==> $k = – 2$.
Standard 11
Mathematics
