If 4{sin ^4}x + {cos ^4}x = 1, then x = | vedclass

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

Question

(a) The given equation can be put in the form

$4{\sin ^4}x = 1 - {\cos ^4}x = (1 - {\cos ^2}x)\,(1 + {\cos ^2}x)$

$ \Rightarrow $ ${\sin ^2}x[4{

Vedclass · Accepted Answer

$n\pi $

Vedclass · Answer

(a) The given equation can be put in the form

$4{\sin ^4}x = 1 - {\cos ^4}x = (1 - {\cos ^2}x)\,(1 + {\cos ^2}x)$

$ \Rightarrow $ ${\sin ^2}x[4{\sin ^2}x - 1 - (1 - {\sin ^2}x)] = 0$

$ \Rightarrow $${\sin ^2}x[5{\sin ^2}x - 2] = 0$

$ \Rightarrow $$\sin x = 0$ or $\sin x = \pm \sqrt {2/5} $.

Hence $x = n\pi $ is the required answer.

If $4{\sin ^4}x + {\cos ^4}x = 1,$ then $x =$

Similar Questions

One of the solutions of the equation $8 \sin ^3 \theta-7 \sin \theta+\sqrt{3} \cos \theta=0$ lies in the interval

The number of solutions that the equation $sin5\theta cos3\theta = sin9\theta cos7\theta$ has in $\left[ {0,\frac{\pi }{4}} \right]$ is

If the solution for $\theta$ of $\cos p\theta + \cos q\theta = 0,\;p > 0,\;q > 0$ are in $A.P.$ , then the numerically smallest common difference of $A.P.$ is

Values of $\theta (0 < \theta < {360^o})$ satisfying ${\rm{cosec}}\theta + 2 = 0$ are

The general value $\theta$ is obtained from the equation $\cos 2\theta = \sin \alpha ,$ is

If 4sin4x+cos4x=1,4{\sin ^4}x + {\cos ^4}x = 1, then x=x =

Similar Questions

One of the solutions of the equation 8sin3θ−7sinθ+√3cosθ=08 \sin ^3 \theta-7 \sin \theta+\sqrt{3} \cos \theta=0 lies in the interval

The number of solutions that the equation sin5θcos3θ=sin9θcos7θsin5\theta cos3\theta = sin9\theta cos7\theta has in [0,π4]\left[ {0,\frac{\pi }{4}} \right] is

If the solution for θ\theta of cospθ+cosqθ=0,p>0,q>0\cos p\theta + \cos q\theta = 0,\;p > 0,\;q > 0 are in A.P.A.P., then the numerically smallest common difference of A.P.A.P. is

Values of θ(0<θ<360o)\theta (0 < \theta < {360^o}) satisfying cosecθ+2=0{\rm{cosec}}\theta + 2 = 0 are