Value of k , for which {(cos x + sin x)^2} + k,sin xcos x - 1 = 0 is an identity, is

English

Gujarati

Hindi

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

Share

Similar Questions

In a right angled triangle the hypotenuse is $2 \sqrt 2$ times the perpendicular drawn from the opposite vertex. Then the other acute angles of the triangle are

normal

If $\sin x + {\rm{cosec}}\,x = 2,$ then $sin^n x + cosec^n x$ is equal to

easy

If $\sin \theta = – \frac{1}{{\sqrt 2 }}$ and $\tan \theta = 1,$ then $\theta $ lies in which quadrant

easy

If $\left| {\,a\,{{\sin }^2}\theta + b\sin \theta \cos \theta + c\,{{\cos }^2}\theta – \frac{1}{2}(a + c)\,} \right|\, \le \frac{1}{2}k,$ then ${k^2}$ is equal to

hard

If $\tan \,(A – B) = 1,\,\,\,\sec \,(A + B) = \frac{2}{{\sqrt 3 }},$ then the smallest positive value of $B$ is

medium