Question

Oblicz sin⁶a+cos⁶α, jeśli sinα·cosα=m !

Answer 1

a = sin^2a

b = cos^2a

a^3+b^3 = (a+b)(a^2-ab+b^2)

a+b = sin^2a+cos^2a = 1

a^2-ab+b^2 = a^2 + b^2 - sin^2a*cos^2a = a^2 + b^2 - (sinacosa)^2 =

= a^2+ b^2 - m^2 = (a+b)^2 - 2*ab -m^2= 1-2*m^2 - m^2 = 1 - 3m^2