Verify this equation

Question

f(x) = sin⁴(x) − cos⁴(x),  g(x) = 2 sin²(x) − 1

Thanks for the help!

Answer 1

Here's a hint to get you started

f(x) = sin⁴x - cos⁴x

= (sin²x - cos²x)(sin²x + cos²x)

Now keep simplifying the above expression