Sin^3 (x) + cos^3 (x) = 1 - 1/2 sin2x

(sinx+cosx) (sin²x-sinxcosx+cos²x) - (1-1/2*2sinxcosx) = 0

(sinx+sin (π/2-x)) (1-sinxcosx) - (1-sinxcosx) = 0

(1-sinxcosx) (2sinπ/4cos (π/4-x) - 1) = 0

1-1/2sin2x=0

1/2sin2a=1⇒sin2x=2∉[-1; 1]-нет решения

√2cos (π/4-x) - 1=0⇒√2cos (π/4-x) = 1⇒cos (π/4-x) = √2/2

π/4-x=π/4+2πn U π/4-x=-π/4+2πn

x=π/4-π/4+2πn U x=π/4+π/4+2πn

x=2πn U x=π/2+2πn