https://www.desmos.com/calculator/6sdbz1iahd
Let $\alpha$ be the angle $XOP$. We know that:
$\sin(\alpha)=PA$, and $\cos(\alpha)=PB$
$\tan(\alpha)=PC$, and $\cot(\alpha)=PD$
$\sec(\alpha)=OC$, and $\csc(\alpha)=OD$
How can we, using geometry, prove that $PC=\frac{PA}{PB}$, prove that $\frac{1}{PA}=OD$, and so on.
I hope you do not consider this as a silly question. I just believe it is (false) to prove these by recalling the trigonometric functions mentioned above.
Your help would be appreciated. THANKS!