Помогииитее(sinx+cosx)^2=1+sinx cosx

Question

Помогииитее

(sinx+cosx)^2=1+sinx cosx

Answer 1

Sin^2x+cos^2x +2sinxcosx-1-sinxcosx=0
1+2sinxcosx-1-sinxcosx=0
sinxcosx=0
sinx=0 или cosx=0
x=пиk        x=пи/2+ пиk 

Answer 2

(sinx+cosx)²=1+sinxcosx
sin²x+2sinxcosx+cos²=sin²x+cos²+sinxcosx
sinxcosx=0
sinx=0 abo cosx=0
x= πk,k∈z   abo x=π\2+πn, n∈z