Proszę o szybką odpowiedź Oblicz funkcję: (tg + ctg)^2 = (1/sin*cos)^2 wiedząc że: Sin^2 + cos ^2=1 Sin/cos=tg Cos/sin=ctg Tg*ctg=1

(tg + ctg)^2 = (1/(sin*cos))^2 (sin/cos + cos/sin)^2 = (1/(sin*cos))^2 (sin*sin/(sin*cos) + cos*cos/(sin*cos))^2 = (1/(sin*cos))^2 ((sin^2 + cos^2) / (sin*cos))^2 = (1/(sin*cos))^2 (1/(sin*cos)))^2 = (1/(sin*cos))^2 L = P

[latex](tgx+ctgx)^{2} = (frac{1}{sinx*cosx})^{2}\\L = (frac{sinx}{cosx}*frac{cosx}{sinx})^{2} = (frac{sin^{2}x+cos^{2}x}{sinxcosx})^{2} =(frac{sin^{2}x+cos^{2}x}{sinxcosx})^{2} =\\=(frac{1}{sinxcosx})^{2} = P\\L = P[/latex]