Prove the Identity: tan²θ - sin²θ = tan²θsin²θ
The Attempt at a Solution
Well I got up to (sin²θ/cos²θ) - (sin²θcos²θ/cos²θ) = sin⁴θ/cos²θ
I got the answer cause my calculator says sin²θ - sin²θcos²θ = sin⁴θ
But I don't know how sin²θ - sin²θcos²θ = sin⁴θ.
How do you subtract sin²θcos²θ with sin²θ?
Also while I'm at it, how does sin⁴θ - cos⁴θ = 1 - 2cos²θ?