Question

Тригонометрия. Упростите выражение (sina/tga)^2+(cosa/tga)^2-2sin^2a

Answer 1

$(frac{sinalpha}{tgalpha})^{2}+(frac{cosalpha}{ctgalpha})^{2}-2sin^{2}alpha=(sinalphacdotfrac{cosalpha}{sinalpha})^{2}+(cosalphacdotfrac{sinalpha}{cosalpha})^{2}\-2sin^{2}alpha=cos^{2}alpha+sin^{2}alpha-2sin^{2}alpha=1-2sin^{2}alpha=cos2alpha$