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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

$-2$

Vedclass · Answer

(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

Similar Questions

If $\cot \theta + \tan \theta = m$ and $\sec \theta - \cos \theta = n,$ then which of the following is correct?

$\frac{{\sin (B + A) + \cos (B - A)}}{{\sin (B - A) + \cos (B + A)}} = $

If $\tan A = \frac{1}{2},$ then $\tan 3A = $

If $7 \sin^{2} \theta + 3 \cos^{2} \theta = 4$,then the value of $\tan \theta$ is (where $\theta$ is acute).

The value of $\frac{\sin 150^{\circ}-5 \cos 300^{\circ}+7 \tan 225^{\circ}}{\tan 135^{\circ}+3 \sin 210^{\circ}}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module