Please help: How to solve this problem using trig identities

[Skylar]

how can i simplify this equation using trig identities/formulas:

cosy = sqrt{sin⁴x + 4cos²x} - sqrt{cos⁴x + 4sin²x}

[stapel_eliz]

cosy = sqrt{sin⁴x + 4cos²x} - sqrt{cos⁴x + 4sin²x}

What are you given as the relationship between "x" and "y"? Thank you!

[Skylar]

I think we are just supposed to simplify the expression on the right side of the equation. The instructions are to "express y in terms of x"

[stapel_eliz]

I think we are just supposed to simplify the expression on the right side of the equation. The instructions are to "express y in terms of x"

Then you're not supposed to simplify; you're supposed to solve for y.

A good start will be to apply the Pythagorean Identity to the quadric terms. For instance, restate (cos²(x))² in terms of sine, and then combine with the other sine term inside that square root. And so forth.

Once you have the right-hand side simplified somewhat, you can take the inverse.