Question

Cos^2x-sin^4x+cos^4x

Answer 1

1) Cos²x - Cos⁴x + Sin⁴x = Cos²x - (Cos⁴x - Sin⁴x) = Cos²x - (Cos²x - Sin²x)(Cos2x + Sin²x) = Cos²x - Cos²x + Sin²x = Sin²x
2) Sin²x - Sin⁴x + Cos⁴x = Sin²x - (Sin²x - Cos²x)(Sin²x + Cos²x) = Sin²x - Sin²x + Cos²x = Cos²x
3) $\frac{1 - Sin ^{2}x }{1 - Cos ^{2}x } + tgx * ctgx = \frac{Cos ^{2}x }{Sin ^{2}x } + 1 = tg ^{2}x + 1 = \frac{1}{Cos ^{2}x }$