Question

тригонометрия √2 cos(x-pi/4)=(sinx+cosx)^2

Answer 1

Пошаговое объяснение:

√2cosxcosπ/4+√2sinxsinπ/4=(sinx+cosx)²

√2*√2/2cosx+√2*√2/2sinx=(sinx+cosx)²

cosx+sinx=(sinx+cosx)²

(sinx+cosx)(sinx+cosx-1)=0

sinx+cosx=0

sinx+sin(π/2-x)=0

2sinπ/4cos(x-π/4)=0

cos(x-π/4)=0

x-π/4=π/2+πn

x=3π/4+ππn

sinx+cosx-1=0

2sinx/2cosx/2+cos²x/2-sin²x/2-sin²x/2-cos²x/2=0

2sinx/2cosx/2-2sin²x/2=0/2cos²x/2≠0

tgx/2-tg²x/2=0

tgx/2(1-tgx/2)=0

tgx/2=0

x/2=πn

x=2πn

tgx/2=1

x/2=π/4+πn

x=π/2+2πn