Question

How do you express `sin^4theta-cos^2theta-tan^2theta` in terms of non-exponential trigonometric functions?

Answer 1

`f(x) = sin^4 x - cos^2 x - tan^2 x =`
`= (sin^2 x - cos x)(sin ^2 x + cos x) - sin^2 x/(cos^2 x)`
Replace
`sin^2 x` by `(1/2)(1 - cos 2x)`
`cos^2 x` by `(1/2)(1 + cos 2x)`
`f(x) = [(1 - cos 2x)/2 - cos x)][(1 - cos 2x)/2 + cos x] - (1 - cos 2x)/(1 + cos 2x)`