Question

Помоги с матешей, 10 класс...

Answer 1

$frac{sin^2t+cos^2t}{tg^2t*cos^2t}-frac{cos^2t}{1-cos^2t}=1; Leftrightarrow frac{1}{sin^2t}-frac{cos^2t}{sin^2t}=1; Leftrightarrow frac{1-cos^2t}{sin^2t}=1; Leftrightarrow frac{sin^2t}{sin^2t}=1; Leftrightarrow 1=1;$

$sint=+-sqrt{1-cos^2t}=-sqrt{1-frac{81}{1681}}=-sqrt{frac{1600}{1681}}=-frac{40}{41};$, т.к. t в четвертой четверти.

$tgt=frac{sint}{cost}=-frac{40}{41}:frac{9}{41}=-frac{40}{9};$

$ctgt=frac{1}{tgt}=1:(-frac{40}{9})=-frac{9}{40};$