solving conditional trig equations

[cotfw]

I can't seem to get this into a form to use the Zero Product property.

Here is the question:

2cos⁴x - sin²x = 0

I thought maybe I could turn sin²x into 1-cos²x and that left me with:

2cos⁴x + cos²x - 1

But I am confused about how to factor further.

 

[Ishuda]

I can't seem to get this into a form to use the Zero Product property.

Here is the question:

2cos⁴x - sin²x = 0

I thought maybe I could turn sin²x into 1-cos²x and that left me with:

2cos⁴x + cos²x - 1

But I am confused about how to factor further.

Let t = cos²(x) and you have a simple quadratic equation
2 t² + t - 1 = 0
Solve for t then
x = cos^-1(t^1/2)

 

[cotfw]

Thank you that cleared it up.