Question

докажите тождество!!!!!
2sin^2α+2cos^2α+tg^2α+ctg^2α= 1/sin^2α*cos^2α

Answer 1

$2Sin^{2}alpha+2Cos^{2}alpha+tg^{2}alpha+Ctg^{2}alpha=2(Sin^{2}alpha+Cos^{2}alpha)+(frac{Sin^{2}alpha}{Cos^{2}alpha}+frac{Cos^{2}alpha}{Sin^{2}alpha})=2+frac{Sin^{4}alpha+Cos^{4}alpha}{Sin^{2}alpha Cos^{2}alpha}=frac{Sin^{4}alpha+2Sin^{2}alpha Cos^{2}alpha+Cos^{4}alpha}{Sin^{2}alpha Cos^{2}alpha}=frac{(Sin^{2}alpha+Cos^{2}alpha)^{2}}{Sin^{2}alpha Cos^{2}alpha} =frac{1}{Sin^{2}alpha Cos^{2}alpha}$

$frac{1}{Sin^{2}alpha Cos^{2}alpha}=frac{1}{Sin^{2}alpha Cos^{2}alpha}$

Тождество доказано