Tg (x+20°)+tg(70°-x) =2 .очень прошу помочь

[latex]tg(x+20)+tg(70-x)=2[/latex] [latex]tg(x+20) + tg(90-20-x) = 2[/latex] [latex]tg(x+20) + ctg(x+20) = 2[/latex] [latex] \frac{sin(x+20)}{cos(x+20)}+ \frac{cos(x+20)}{sin(x+20)} = \frac{ sin^{2}(x+20)+cos^{2}(x+20) }{cos(x+20)sin(x+20)} =2[/latex] [latex] \frac{1}{cos(x+20)sin(x+20)}=2 [/latex] 2cos(x+20)sin(x+20) = 1 sin(2x+40) = 1 2x + 40 = [latex] \frac{ \pi }{2}+2 \pi n [/latex] 2x = 45 -40 +[latex]2 \pi n[/latex] x = 2,5 + [latex] \pi n[/latex],    n∈Z