Oftentimes, your math teachers will ask you to prove equalities that involve the secant, cosecant, or cotangent functions. Whenever you see these functions in a proof, the reciprocal identities usually are the best places to start. Without the reciprocal identities, you can go in circles all day without ever actually getting anywhere.
For example, to prove
![image0.png](https://www.dummies.com/wp-content/uploads/370329.image0.png)
you can work with the left side of the equality only. Follow these simple steps:
Convert all functions to sines and cosines.
The left side of the equation now looks like this:
Cancel all possible terms.
Canceling gives you
which simplifies to
You can't leave the reciprocal function in the equality, so convert back again.