Salut,
[tex]tgB+ctgB=\dfrac{sinB}{cosB}+\dfrac{cosB}{sinB}=\dfrac{sin^2B+cos^2B}{sinB\cdot cosB}=\dfrac{1}{sinB\cdot cosB}\Rightarrow\\\\\Rightarrow sinB\cdot cosB=\dfrac{1}5;\\\\(sinB+cosB)^2=sin^2B+2\cdot sinB\cdot cosB+cos^2B=1+2\cdot sinB\cdot cosB=\\\\=1+2\cdot\dfrac{1}{5}=\dfrac{7}{5}\Rightarrow sinB+cosB=\pm\sqrt{\dfrac{7}5};\\\\(tgB+ctgB)^2=tg^2B+2\cdot tgB\cdot ctgB+ctg^2B=tg^2B+ctg^2B+2\Rightarrow\\\\\Rightarrow tg^2B+ctg^2B=(tgB+ctgB)^2-2=25-2=23.[/tex]
Green eyes.
