The total number of solution of sin^4x + cos^ | vedclass

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

Question

$\sin ^{4} x+\cos ^{4} x=\sin x \cos x$

or $\left(\sin ^{2} x+\cos ^{2} x\right)^{2}-2 \sin ^{2} x \cos ^{2} x=\sin x \cos x$

or $1-\frac{\sin ^

Vedclass · Accepted Answer

$2$

Vedclass · Answer

$\sin ^{4} x+\cos ^{4} x=\sin x \cos x$

or $\left(\sin ^{2} x+\cos ^{2} x\right)^{2}-2 \sin ^{2} x \cos ^{2} x=\sin x \cos x$

or $1-\frac{\sin ^{2} 2 x}{2}=\frac{\sin 2 x}{2}$

or $\sin ^{2} 2 x+\sin 2 x-2=0$

$\operatorname{or}(\sin 2 x+2)(\sin 2 x-1)=0$

or $\sin 2 x=1$

or $2 \mathrm{x}=(4 \mathrm{n}+1) \frac{\pi}{2}, \mathrm{n} \in \mathrm{Z}$

or $x=(4 n+1) \frac{\pi}{4}, n \in Z$

$=\frac{\pi}{4}, \frac{5 \pi}{4} \quad(\because x \in[0,2 \pi])$

Thus, there are two solutions.

The total number of solution of $sin^4x + cos^4x = sinx\, cosx$ in $[0, 2\pi ]$ is equal to

Similar Questions

The value of the expression

$\frac{{\left (sin 36^o + cos 36^o - \sqrt 2 sin 27^o)( {\sin {{36}^0} + \cos {{36}^0} - \sqrt 2 \sin {{27}^0}} \right)}}{{2\sin {{54}^0}}}$ is less than

The general value of $\theta $ in the equation $2\sqrt 3 \cos \theta = \tan \theta $, is

If $\sqrt 3 \cos \,\theta + \sin \theta = \sqrt 2 ,$ then the most general value of $\theta $ is

If $|cos\ x + sin\ x| + |cos\ x\ -\ sin\ x| = 2\ sin\ x$ ; $x \in [0,2 \pi ]$ , then maximum integral value of $x$ is

If $\sin \,\theta + \sqrt 3 \cos \,\theta = 6x - {x^2} - 11,x \in R$ , $0 \le \theta \le 2\pi $ , then the equation has solution for