Sabendo que:
[tex]\boxed{\sf tg(x)~=~\dfrac{sen(x)}{cos(x)}}\boxed{\sf sec(x)~=~\dfrac{1}{cos(x)}}\boxed{\sf cossec(x)~=~\dfrac{1}{sen(x)}}[/tex]
Temos:
[tex]\sf tg(x)\cdot cos(x)\cdot sec(x)\cdot cossec(x)~=~\dfrac{sen(x)}{cos(x)}\cdot cos(x)\cdot \dfrac{1}{cos(x)}\cdot \dfrac{1}{sen(x)}\\\\\\\sf tg(x)\cdot cos(x)\cdot sec(x)\cdot cossec(x)~=~\dfrac{sen(x)\cdot cos(x)\cdot 1\cdot 1~\,}{cos(x)\cdot cos(x)\cdot sen(x)}[/tex]
[tex]\sf tg(x)\cdot cos(x)\cdot sec(x)\cdot cossec(x)~=~\dfrac{\not\!\!\!sen(x)\cdot cos(x)}{cos(x)\cdot cos(x)\cdot \not\!\!\!sen(x)}\\\\\\\sf tg(x)\cdot cos(x)\cdot sec(x)\cdot cossec(x)~=~\dfrac{\not\!\!\! cos(x)}{cos(x)\cdot \not\!\!\!cos(x)}\\\\\\\sf tg(x)\cdot cos(x)\cdot sec(x)\cdot cossec(x)~=~\dfrac{1}{cos(x)}\\\\\\\boxed{\sf \sf tg(x)\cdot cos(x)\cdot sec(x)\cdot cossec(x)~=~sec(x)}[/tex]
[tex]\Huge{\begin{array}{c}\Delta \tt{\!\!\!\!\!\!\,\,o}\!\!\!\!\!\!\!\!\:\,\perp\end{array}}Qualquer~d\acute{u}vida,~deixe~ um~coment\acute{a}rio[/tex]
