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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Jennifer (Customer)

[00:00:00] Complete the last step to prove the following identity. Express in terms of tan and/or cot.
1 + tan^2 x/tan^2 x = csc^2x. Answer: _____^2 ____ = csc^2 x.

Elizabeth C (Tutor)

[00:00:27] Hi!
I can see you posted a problem, how can I help you with it?

Jennifer (Customer)

[00:00:50] I basically just need help
solving the problem...

Elizabeth C (Tutor)

[00:01:07] Sure, no problem.
Do you have an idea where to start?

Jennifer (Customer)

[00:01:56] well, I know that we just need
to use trigonometric equations
to solve for csc^2x.

Elizabeth C (Tutor)

[00:02:12] Sounds good.

[00:02:24] Shall we work with the left side, since it's a little more complicated?

Jennifer (Customer)

[00:02:45] sure.

Elizabeth C (Tutor)

[00:02:55] Great

[00:03:47] Let's start with that.
There are several ways you can do this, so... Where do you want to start?

Jennifer (Customer)

[00:04:25] well would the Tan's cancel
each other?

Elizabeth C (Tutor)

[00:04:51] Not quite, but we can work with that idea if you'd like

Jennifer (Customer)

[00:05:10] ok.

Elizabeth C (Tutor)

[00:05:42] We can break up the fraction first, and then you might be able to cancel

Jennifer (Customer)

[00:05:54] ok.

Elizabeth C (Tutor)

[00:06:20] How does that look?

Jennifer (Customer)

[00:06:28] good.

Elizabeth C (Tutor)

[00:06:49] Ok, so what do you want to do from here?

Jennifer (Customer)

[00:07:22] do those two cancel?

[00:07:34] and leave us with 1/tan^2 x?

Elizabeth C (Tutor)

[00:07:54] The tan^2 x/tan^2 x would cancel to become 1.

Jennifer (Customer)

[00:07:59] ok.

Elizabeth C (Tutor)

[00:08:17] So you're left with 1/tan^2x +1

Jennifer (Customer)

[00:08:26] ok.

Elizabeth C (Tutor)

[00:08:28] What's your next step?

Jennifer (Customer)

[00:08:53] thinking...

[00:09:29] would 1/tan^2x become
cot^2x?

Elizabeth C (Tutor)

[00:09:38] Yes it would

Jennifer (Customer)

[00:09:58] cool!

Elizabeth C (Tutor)

[00:10:08] And the last step is?

Jennifer (Customer)

[00:10:38] it then becomes csc^2 x.

Elizabeth C (Tutor)

[00:10:54] Yep!

Jennifer (Customer)

[00:11:01] Awesome!

Elizabeth C (Tutor)

[00:11:18] Anything else I can help you with today?

Jennifer (Customer)

[00:12:10] No, thank you.

[00:12:14] Have a great day!

[00:12:18]

Elizabeth C (Tutor)

[00:12:22] You're welcome.
Have a great evening!

Jennifer (Customer)

[00:12:38] U2.