1. ## Trig Problem

[sec(theta)*csc(theta)=2csc(theta)

I have been working on this problem forever, and I finally decided to seek help. My first thought upon seeing this problem was to divide both sides by csc(theta) leaving the equation as sec(theta)=csc(theta), but that isn't the right answer. For some reason the answer seems obvious, but I can't find it. Can someone help me please?

I really want to work it out myself, but can someone just nudge me in the right direction?

2. $\displaystyle \sec{t} \csc{t} = 2\csc{t}$

$\displaystyle 0 = 2\csc{t} - \sec{t}\csc{t}$

$\displaystyle 0 = \csc{t}(2 - \sec{t})$

$\displaystyle \csc{t}$ is never 0, so $\displaystyle \sec{t} = 2$

can you finish?

3. Thank you so much!! These problems have always been a pain for me.

One more question. Is the reason csc(theta) is never equal to zero because it would be undefined?

4. $\displaystyle \csc{t} = \frac{1}{\sin{t}}$

will any value of $\displaystyle \sin{t}$ (which are between -1 and 1) ever make the right side of the above equation equal 0?

5. It would depend on if you are talking about an angle (theta) or an unknown value (such as t) right?

Since csc=r/y, with r=1 on the unit circle, y would equal 0 at 2pi and/or 0.

I think I'm starting to confuse myself.

6. you're making this too hard ... it doesn't matter what the angle theta is.

bottom line is that csct = 1/sint, and 1 divided by anything between -1 and 1 can never equal 0.

7. I tend to do that.

Thank you for helping.