Question

pe asta cum o fac ????? plz help x apartine de la 0 la pi/2​

Answer 1

$\frac{1+sin^{2}x}{2+ctg^{2}x}+\frac{1+cos^{2}x}{2+tg^{2}x}=\frac{1+sin^{2}x}{2+\frac{cos^{2}x}{sin^2{x}}}+\frac{1+cos^{2}x}{2+\frac{sin^{2}x}{cos^{2}x}}$$=\frac{1+sin^{2}x}{\frac{2sin^{2}x+cos^{2}x}{sin^{2}x}}+\frac{1+cox^{2}x}{\frac{2cox^{2}x+sin^{2}x}{cox^{2}x}}=$$=\frac{1+sin^{2}x}{\frac{sin^{2}x+1}{sin^{2}x}}+\frac{1+cox^{2}x}{\frac{cox^{2}x+1}{cox^{2}x}}=$$sin^{2}x+cos^{2}x=1$