# What identity should I use?

• Mar 7th 2010, 04:17 PM
mtt0216
What identity should I use?
What Identity should I use to solve this.

$\displaystyle csc x-\frac{cotx}{secx} =sinx$
• Mar 7th 2010, 04:20 PM
mr fantastic
Quote:

Originally Posted by mtt0216
What Identity should I use to solve this.

$\displaystyle csc x-\frac{cotx}{secx} =sinx$

You are not solving anything. You are proving an identity. There's a big difference in meaning between these two words.

I suggest you substitute the definitions of csc x, cot x and sec x into the left hand side and simplify the result.
• Mar 8th 2010, 10:46 AM
mtt0216
I meant to say prove sorry about that.

The problem I have with this problem is that I don't know how to change

$\displaystyle \frac{cotx}{secx}$ into a different form.

Its just the fact thats its in an equation and I just don't know where to start.
• Mar 8th 2010, 10:54 AM
mr fantastic
Quote:

Originally Posted by mtt0216
I meant to say prove sorry about that.

The problem I have with this problem is that I don't know how to change

$\displaystyle \frac{cotx}{secx}$ into a different form.

Its just the fact thats its in an equation and I just don't know where to start.

Do you know the definition of each in terms of sinx and cosx? It will be in your notes and/or textbook. Then make the substitutions as I said in my first reply.
• Mar 8th 2010, 11:17 AM
mtt0216
I know the definitions:

csc x = 1/sinx

sec x = 1/cosx

Cot= cosx/sinx

But once I put them into the equation I dont know what to do.
• Mar 8th 2010, 11:20 AM
mr fantastic
Quote:

Originally Posted by mtt0216
I know the definitions:

csc x = 1/sinx

sec x = 1/cosx

Cot= cosx/sinx

But once I put them into the equation I dont know what to do.

At this level you should be able to do basic algebra on expressions like (a/b)/(c/d) to get (ad)/(bc).

Note: $\displaystyle \frac{a/b}{c/d} = \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = ....$
• Mar 8th 2010, 11:27 AM
mtt0216
Quote:

Originally Posted by mr fantastic
At this level you should be able to do basic algebra on expressions like (a/b)/(c/d) to get (ad)/(bc).

Note: $\displaystyle \frac{a/b}{c/d} = \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = ....$

OK sorrryy that I forgot a basic step.......................
• Mar 8th 2010, 11:42 AM
bigwave
Quote:

Originally Posted by mtt0216
I know the definitions:

csc x = 1/sinx

sec x = 1/cosx

Cot= cosx/sinx

But once I put them into the equation I dont know what to do.

$\displaystyle \frac{1}{\sin{\theta}} -\frac {\frac{\cos{\theta}}{\sin{\theta}}} {\frac{1}{\cos{\theta}}} \rightarrow \frac{1}{\sin{\theta}}-\frac{\cos{\theta}}{\sin{\theta}} \frac{\cos{\theta}}{1} \rightarrow \frac{1-\cos^2{\theta}}{\sin{\theta}} \rightarrow \frac{\sin^2{\theta}}{\sin{\theta}}= \sin{\theta}$