Question

Упростите вырожения: sin t * cos t * (tg t + ctg t)

Answer 1

Решение:
$sintcost(frac{sint}{cost}+frac{cost}{sint})=sintcost*frac{sin^2t+cos^2t}{sintcost}=sin^2t+cos^2t=1$

Answer 2

sin t*cos t*(sin t/cos t+ cos t/sin t)=sin t*cos t*((sin^2 t+cos^2t)/cos t*sin t)=
sin t*cos t*(1/sin t*cos t)=1                                sin^2 t+ cos^2 t=1 по основному       
Ответ:1                                                            тригонометрическому тождеству