Sina-cosa=a то sin⁴a+cos⁴a=?

(sina-cosa) ^2 = 1 - 2sina*cosa = a^2 - >

2sina*cosa = 1-a^2

(sin^2a+cos^2a) ^2 = 1 - > sin^4a+cos^4a+2sin^2a*cos^2a = 1

-> sin^4a+cos^4a = 1 - 2sin^2a*cos^2a = 1 - ((1-a^2) ^2) / 2 =

(2-1+2a^2 - a^4) / 2 = (1+2a^2 - a^4) / 2

sin^a+cos^4a = (1+2a^2 - a^4) / 2