Answer:
cosecx
Step-by-step explanation:
[tex] \frac{cotx}{cosx} \\ = \frac{1}{tanx} \div cosx \\ = (1 \div \frac{sinx}{cosx} ) \div cosx \\ = \frac{cosx}{sinx} \times \frac{1}{cosx} \\ = \frac{1}{sinx} \\ = cosecx[/tex]
Note that:
[tex]tanx = \frac{sinx}{cosx} [/tex]
[tex]cotx = \frac{1}{tanx} = \frac{cosx}{sinx} [/tex]
[tex]cosecx = \frac{1}{sinx} [/tex]
