Question

Решите тригонометрическое уравнение 99 отдала cosx/4×sinπ/5-sinx/4×cosπ/5=√2/2

Answer 1

$cos \frac{x}{4} *sin \frac{ \pi }{5} -sin \frac{x}{4}*cos \frac{ \pi }{5}= \frac{ \sqrt{2} }{2}$

$sin( \frac{ \pi }{5} - \frac{x}{4})= \frac{ \sqrt{2} }{2}$

$-sin( \frac{x}{4}- \frac{ \pi }{5} )= \frac{ \sqrt{2} }{2}$

$sin( \frac{x}{4}- \frac{ \pi }{5} )=- \frac{ \sqrt{2} }{2}$

$\frac{x}{4}- \frac{ \pi }{5}=(-1)^narcsin(- \frac{ \sqrt{2} }{2})+ \pi n,$ $n$ ∈ $Z$

$\frac{x}{4}- \frac{ \pi }{5}= (-1)^{n+1} *\frac{ \pi }{4} + \pi n,$ $n$ ∈ $Z$

$\frac{x}{4}= (-1)^{n+1}*\frac{ \pi }{4} + \frac{ \pi }{5} + \pi n,$ $n$ ∈ $Z$

$x= (-1)^{n+1} *\pi + \frac{ 4\pi }{5} + 4\pi n,$ $n$ ∈ $Z$

Answer 2

Sinxcosy-cosxsiny=sin(x-y)
cosx/4*sinπ/5-sinπ/4*cosπ/5=0
sin(π/5-x/4)=√2/2
-sin(x/4-π/5)=√2/2
sin(x/4-π/5)=-√2/2
x/4-π/5=(-1)^(n+1)*π/4+πn,n∈z
x/4=(-1)^(n+1)*π/4+π/5+πn,n∈z
x=(-1)^(n+1)*π+4π/5+4πn,n∈z