Question

What is Cot(x) / cos(x) ?

Answer 1

Answer:

cosecx

Step-by-step explanation:

$\frac{cotx}{cosx} \\ = \frac{1}{tanx} \div cosx \\ = (1 \div \frac{sinx}{cosx} ) \div cosx \\ = \frac{cosx}{sinx} \times \frac{1}{cosx} \\ = \frac{1}{sinx} \\ = cosecx$

Note that:

$tanx = \frac{sinx}{cosx}$

$cotx = \frac{1}{tanx} = \frac{cosx}{sinx}$

$cosecx = \frac{1}{sinx}$