Sina-cosa=a то sin⁴a+cos⁴a=?

Question

Sina-cosa=a то sin⁴a+cos⁴a=?

Answer 1

(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