SOLUTION
The difference be tween the trigonometrical identities can be defined by stating their ratios of the sides of a right triangle.
Consider the right triangle below
Using the trigonometrical ratios,
SOH CAH TOA
it follows:
[tex]\begin{gathered} \sin\theta=\frac{c}{b} \\ \cos\theta=\frac{a}{b} \\ \tan\theta=\frac{c}{a} \end{gathered}[/tex]Using the derived ratios, it follows
[tex]\begin{gathered} \csc\theta=\frac{1}{\sin\theta}=\frac{b}{c} \\ \sec\theta=\frac{1}{\cos\theta}=\frac{b}{a} \\ \cot\theta=\frac{1}{\tan\theta}=\frac{a}{c} \end{gathered}[/tex]The ratios shows the differences.
