Simplify the following expression by writing it in terms of sine or cosine only:
\[
\frac{1}{\csc (x)}-\cot (x)=
\]

Answer

Expert–verified

Hide Steps

Answer

Finally, we can write this as \[\boxed{1 - \cot x}\]

Steps

Step 1 ：We can write \[\frac{1}{\csc (x)}-\cot (x) = \frac{\sin x}{1} - \frac{\cos x}{\sin x}\]

Step 2 ：This simplifies to \[\frac{\sin x - \cos x}{\sin x}\]

Step 3 ：Finally, we can write this as \[\boxed{1 - \cot x}\]