Mastering Identities: Solving Tricky Problems in Pre-Cal 2

[msdenise15]

Hi,

I'm new to this site and I'm very happy that I found it. My Pre-cal 2 teacher has been no help to me when it comes to explaining certain steps needed to solve a problem. Overall I'm having a hard time choosing the correct identity needed to solve the problems. However what I do not understand about this particular problem is how to change the denominator.

The question is:

Sec/Tan -Tan/Sec = cosxcotx

I started by expanding sec and tan which gave me (1/cos)/(sin/cos)-(cos/sin)/(1/cos)

but what should I do to change the denominator?

 

[quantumdude]

That's a good start. Now think back to arithmetic: What do you do when you are asked to divide two fractions? I ask this, because that's exactly what you have there. For instance:

$$\frac{\frac{1}{\cos(x)}}{\frac{\sin(x)}{\cos(x)}}=\frac{1}{\cos(x)}\div\frac{\sin(x)}{\cos(x)}$$

Does that help?