Verified answer

Объяснение:

13.

{x+y=π => y=π-x

{sin(π-x)+siny=2

sin(π-x)+sin(π-x)=2

sinx+sinx=2

2sinx=2

sinx=1

x=π/2+2πn,n∈z

y=π-π/2-2πn,n∈z

y=π/2-2πn,n∈z

ответ: (π/2+2πn; π/2-2πn),n∈z

14.

{x+y=π/2 => y=π/2-x

sin²x-sin²y=√2/2

sin²x-sin(π/2-x)²=√2/2

sin²x-cos²x=√2/2

-cos2x=√2/2

cos2x= -√2/2

2x=3π/4+2πn,n∈z

x=3π/8+πn,n∈z

y=π/2-3π/8-πn,n∈z

y=π/8-πn,n∈z

ответ:(3π/8+πn; π/8-πn) n∈z

15.

{x+y=π => y=π-x

{sin²x+sin²x=1/2

sin²x+sin²x=1/2=> 2sin²x=1/2 => sin²x=1/4=>

=>sinx=±1/2

sinx=1/2 sinx= -1/2

x=7π/6+2πn,n∈z x=π/6+2πn,n∈z

x=11π/6+2πn,n∈z x=5π/6+2πn,n∈z

x=π/6+πn,n∈z

x=5π/6+πn,n∈z

y=π-π/6-πn,n∈z

y=π-5π/6-πn,n∈z

y=5π/6-πn,n∈z

y=π/6-πn,n∈z

ответ: (π/6+πn ; 5π/6-πn),n∈z

(5π/6+πn; π/6-πn),n∈z