Решите тригонометрическое уравнение cosx/4×sinπ/5-sinx/4×cosπ/5=√2/2

Question

Решите тригонометрическое уравнение
cosx/4×sinπ/5-sinx/4×cosπ/5=√2/2

Answer 1

Sinxcosy-cosxsiny=sin(x-y)
sin(π/5-x/4)=√2/2
cos(π/5+x/4)=√2/2
x/4+π/5=-π/4+2πn U x/4+π/5=π/4+2πn
x/4=-π/4-π/5+2πn U x/4=π/4-π/5+2πn
x/4=-9π/20+2πn U x/4=π/20+2πn
x=-9π/5+8πn U x=π/5+8πn,n∈z