Question

Se Tangente X=2, Calcule o valor de cossec²X
(Tem 2 jeito de fazer um mais curto e outro mais longo preciso dos dois jeitos)

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\sf modo~\bf flash\!:}\\\sf tg(x)=2\implies tg^2(x)=4\\\sf cotg^2(x)=\dfrac{1}{4}\\\\\sf cossec^2(x)=1+cotg^2(x)\\\sf cossec^2(x)=1+\dfrac{1}{4}\\\\\sf cossec^2(x)=\dfrac{5}{4}\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\sf modo\,\bf lesma\!:}\\\sf tg(x)=2\\\\\sf\dfrac{sen(x)}{cos(x)}=2\\\\\sf sen(x)=2cos(x)\\\sf sen^2(x)+cos^2(x)=1\\\sf (2cos(x))^2+cos^2(x)=1\\\sf 4cos^2(x)+cos^2(x)=1\\\sf 5cos^2(x)=1\\\sf\\\sf cos^2(x)=\dfrac{1}{5}\\\\\sf sen^2(x)=1-cos^2(x)\\\sf sen^2(x)=1-\dfrac{1}{5}\\\\\sf sen^2(x)=\dfrac{4}{5}\\\sf cossec^2(x)=\dfrac{1}{sen^2(x)}\\\\\sf cossec^2(x)=\dfrac{1}{\dfrac{4}{5}}\\\\\sf cossec^2(x)=\dfrac{5}{4}\end{array}}$