Question

найти tga если (3sina-5cosa+2)/(sina+3cosa+6)=1/3

Answer 1

3sina-5cosa+2sina+3cosa+6=13

=>

9sina-15cosa+6=sina+3cosa+6

=>

8sina=18cosa

=>

sinacosa=188=94=2,25

=>

tga=2,25

Answer 2

$frac{3sin a-5cos a+2}{sin a+3cos a+6}=frac{1}{3}$
$3(3sin a-5cos a+2)=1*(sin a+3cos a+6)$
$9sin a-15cos a+6=sin a+3cos a+6$
$9sin a-15cos a=sin a+3cos a$
$9sin a-sin a=3cos a+15cosa$
$8 sin a=18 cos a$
$tg a=frac{18}{8}=2.25$
$tg a=2.25$