Let S be the sum of all solutions (in radians | vedclass

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

Question

Given equation

$\sin ^{4} 	heta+\cos ^{4} 	heta-\sin 	heta \cos 	heta=0$

$\Rightarrow 1-\sin ^{2} 	heta \cos ^{2} 	heta-\sin 	heta \cos \

Vedclass · Accepted Answer

$56$

Vedclass · Answer

Given equation

$\sin ^{4} 	heta+\cos ^{4} 	heta-\sin 	heta \cos 	heta=0$

$\Rightarrow 1-\sin ^{2} 	heta \cos ^{2} 	heta-\sin 	heta \cos 	heta=0$

$\Rightarrow 2-(\sin 2 	heta)^{2}-\sin 2 	heta=0$

$\Rightarrow(\sin 2 	heta)^{2}+(\sin 2 	heta)-2=0$

$\Rightarrow(\sin 2 	heta+2)(\sin 2 	heta-1)=0$

$\Rightarrow \sin 2 	heta=1 	ext { or } \sin 2 	heta=-2$ $ightarrow$ not possible

$\Rightarrow \quad 2 	heta=\frac{\pi}{2}, \frac{5 \pi}{2}, \frac{9 \pi}{2}, \frac{13 \pi}{2}$

$\Rightarrow \quad 	heta=\frac{\pi}{4}, \frac{5 \pi}{4}, \frac{9 \pi}{4}, \frac{13 \pi}{4}$

$\Rightarrow \frac{8 S}{\pi}=\frac{8 	imes 7 \pi}{\pi}=56.00$

Let $S$ be the sum of all solutions (in radians) of the equation $\sin ^{4} \theta+\cos ^{4} \theta-\sin \theta \cos \theta=0$ in $[0,4 \pi]$ Then $\frac{8 \mathrm{~S}}{\pi}$ is equal to ...... .

Similar Questions

If $0\, \le \,x\, < \frac{\pi }{2},$ then the number of values of $x$ for which $sin\,x -sin\,2x + sin\,3x=0,$ is

The number of solutions of the given equation $\tan \theta + \sec \theta = \sqrt 3 ,$ where $0 < \theta < 2\pi $ is

All the pairs $(x, y)$ that satisfy the inequality ${2^{\sqrt {{{\sin }^2}{\kern 1pt} x - 2\sin {\kern 1pt} x + 5} }}.\frac{1}{{{4^{{{\sin }^2}\,y}}}} \leq 1$ also Satisfy the equation

The value of $\theta $ satisfying the given equation $\cos \theta + \sqrt 3 \sin \theta = 2,$ is

The value of expression $\frac{{2(\sin {1^o} + \sin {2^o} + \sin {3^o} + ..... + \sin {{89}^o})}}{{2(\cos {1^o} + \cos {2^o} + .... + \cos {{44}^o}) + 1}}$ equals