Question

¿Como soluciono está identidad trigonométrica?

Answer 1

${\left(\dfrac{1}{\cos(x)}+\dfrac{\sin(x)}{\cos(x)}\right)^2=}\\\\\\{\left(\dfrac{1+\sin(x)}{\cos(x)}\right)^2=}\\\\\\{\dfrac{(1+\sin(x))^2}{\cos^2(x)}=\ \ \ \ \ \ \boxed{ \text{Recordar: }\cos^2(x)=1-\sin^2(x)=(1-\sin(x))(1+\sin(x))}}\\\\\\{\dfrac{(1+\sin(x))(1+\sin(x))}{(1-\sin(x))(1+\sin(x))}=}\\\\\\{\boxed{\boxed{\dfrac{1+\sin(x)}{1-\sin(x)}}}}\\\\\\{\mathtt{salu2.}}$