Question

Demonstre as seguintes identidades trigonométricas:
a)cos x.tg x. cossec x=1
b)tg²x. cossec² x =1 + tg² x

Answer 1

a)
$cos(x).tg(x).cossec(x)= \\ \\ cos(x).\frac{sen(x)}{cos(x)}.\frac{1}{sen(x)}= 1$

b)
$tg^2(x).cossec^2(x)=1+tg^2(x) \\ \\ \frac{sen^2(x)}{cos^2(x)}.\frac{1}{sen^2(x)}=cossec^2(x) \\ \\ \frac{1}{cos^2(x)}=cossec^2(x) \\ \\ cossec^2(x)=cossec^2(x)$