Question

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

Answer 1

(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