Question

решить тригонометрическое уравнение через разложение на множители
sin (П/12 + х) + sin (П/4-х)=1

Answer 1

2sin[(π/12+x+π/4-x)/2]*cos[(π/12+x-π/4+x)/2]=1
2sin(π/6)*cos(x-π/12)=1
2*1/2*cos(x-π/12)=1
cos(x-π/12)=1
x-π/12=2πk
x=π/12+2πk,k∈z

Answer 2

2sin ( π/12+x+π/4-x /2) *cos ( π/12+x-π/4+x /2 ) =1

2sin π/6 * cos ( 2x-π/6/2)=1

2sin π/6 * cos ( x-π/12)=1

cos(x-π/12)=1
x-π/12=2πn
x=π/12+2πn