Question

решите систему уравнений
$\left \{ {{x+y= \frac{3}{4} \pi } \atop {tgx-tgy=2}} \right.$

Answer 1

y=3/4π -x
tqx-tq(3/4π -x)=2
tqx +tq(x-3/4π)=2
tqx+(tqx-tq3/4)/(1+tqx*tq3/4π) =2
tqx+(1+tqx )/(1-tqx) =2
tqx - tq²x +1+tqx=2-2tqx
tq²x -4tqx +1 =0
tqx₁ =2 - √3 ;    x₁ =arctq(2 - √3)+π*k ; y₁=3/4π -arctq(2 - √3)+π*k
 tqx₂ =2 + √3 ;  x₂ =arctq(2 + √3) +π*k ;y₂=3/4π -arctq(2 + √3)+π*k