[tex]tg^210+2tg10tg70=tg^210+2tg10ctg(90-70)=tg^210+2tg10 \frac{1}{tg20} [/tex], dar tg2α=[tex] \frac{2tg \alpha }{1-tg^2 \alpha } [/tex]. deci [tex] tg20= \frac{2tg10}{1-tg^210} [/tex]. Inlocuind in ultima relatie se obtine dupa rasturnarea fractiei si simplificarii cu 2tg10 : [tex]tg^210+1-tg^210=1.[/tex], ceea ce aveam de demonstrat.
