Question

sabendo que tg x = raiz quadrada de 2 e pertence ao 3 quadrante calcule
sec x e cossec x

Answer 1

$\Large\boxed{\begin{array}{l}\sf tg(x)=\sqrt{2}\implies tg^2(x)=2\\\sf sec^2(x)=1+tg^2(x)\\\sf sec^2(x)=1+2\\\sf sec^2(x)=3\\\sf sec(x)=-\sqrt{3}\\\sf tg(x)= sen(x)\cdot sec(x)\\\sf \sqrt{2}=sen(x)\cdot(-\sqrt{3})\\\sf sen(x)=-\dfrac{\sqrt{2}}{\sqrt{3}}\\\\\sf cossec(x)=-\dfrac{\sqrt{3}}{\sqrt{2}}=-\dfrac{\sqrt{6}}{2}\end{array}}$