Sin^2a - cos^2a + cos^4a\cos^2a -sin^2a+sin^4a

Question

Sin^2a - cos^2a + cos^4a\cos^2a -sin^2a+sin^4a

Answer 1

(Sin²a - Cos²a + Cos⁴a) / (Cos²a - Sin²a + Sin⁴a) = 
= [Sin²a - Cos²a*(1 - Cos²a)] / [Cos²a - Sin²a*(1 - Sin²a)] = 
= (Sin²a - Cos²aSin²a) / (Cos²a - Sin²aCos²a) =
= [Sin²a(1 - Cos²a)] / [Cos²a(1 - Sin²a)] = Sin⁴a / Cos⁴a = tg⁴a