How to solve 2cos^4(x)-sin^2(x)=0? I don't know which identities to use

Question

anonymous · Answer

You can simplify the left hand using $$\cos^2x+\sin^2x=1$$
and treat it like a polynomial and go from there

anonymous · Answer

probably want to turn $\cos^4(x)$ in to something with $\sin^2(x)$ is  my first guess

anonymous · Answer

oh maybe i am wrong

anonymous · Answer

would i move sin^2x to the other side in order to factor out a cos^2x?

jim_thompson5910 · Answer

This is one way to do it
$$\Large 2\cos^4(x)-\sin^2(x)=0$$
$$\Large 2\cos^4(x)-(1-\cos^2(x))=0$$
$$\Large 2\cos^4(x)-1+\cos^2(x)=0$$
$$\Large 2\cos^4(x)+\cos^2(x)-1=0$$
$$\Large 2(\cos^2(x))^2+\cos^2(x)-1=0$$
$$\Large 2z^2+z-1=0 ... \text{Let } z = \cos^2(x)$$
Use the quadratic formula to solve for z. Then use the solutions for z to find the solutions for x.

anonymous · Answer

thanks @jim_thompson5910 , i didn't look at it as a quadratic before! and thanks to everybody else too for helping

jim_thompson5910 · Answer

you're welcome