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.

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

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