Question

Найти 1-sin²α/1+sin2α ,если tgα=-5

Answer 1

$frac{1-sin^2alpha} {1-sin2alpha} =frac{cos^2alpha} {1-2sinalpha cosalpha }=frac{cos^2alpha} {sin^2 alpha + cos^2 alpha - 2 sin alpha cos alpha }= frac{cos^2alpha} {(sinalpha-cosalpha)^2 }=$

$= frac{ frac{cos^2 alpha }{cos^2 alpha }}{( frac{sin alpha }{cos alpha }- frac{cos alpha }{cos alpha })^2 }= frac{1}{(tg alpha- 1)^2 } =frac{1}{(-5- 1)^2 }=frac{1}{36 }$