Question

Решите, пожалуйста cos(п/4+x)*sin(п/4-x)=0,75

Answer 1

sin(π/4-x)=cos(π/4+x)
cos²(π/4+x)=3/4
(cos(π/4+x)-√3/2)(cos(π/4+x)+√3/2)=0
cos(π/4+x)=√3/2
π/4+x=-π/6+2πn U π/4+x=π/6+2πn
x=-5π/12+2πn,n∈z U x=-π/12+2πn,n∈z
cos(π/4+x)=-√3/2
π/4+x=-5π/6+2πn U π/4+x=5π/6+2πn
x=-13π/12+2πn,n∈z U x=7π/12+2πn,n∈z