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System Message

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

Guest (Customer)

[00:00:00]
I have to verify the identity: cos^2(theta) ((sec^2(theta)-1).I started but I got stuck.

Lauren R (Tutor)

[00:00:13] Welcome to Tutor.com ! How can I help you today?

Guest (Customer)

[00:00:51] Hello.I tried to solve the
problem above but I got stuck
at one point.

Lauren R (Tutor)

[00:01:13] would you
mind showing me what you have done so far?

Guest (Customer)

[00:01:30] sure

[00:02:47] sorry, I forgot to add the last
part

Lauren R (Tutor)

[00:03:03] that's ok, I got it now

[00:03:51] ok good so far

[00:04:06] did you get stuck here?

Guest (Customer)

[00:04:19] OK.yes, this is where I got a
little confused

Lauren R (Tutor)

[00:04:29] ok, well let's look at this..

[00:04:37] What do you know about cos and sec?

[00:04:41] what is their relationship?

Guest (Customer)

[00:05:04] cos=1/sec....sec=1/cos?

Lauren R (Tutor)

[00:05:13] yes, so look what I can do..

[00:05:40] it works for squared just like single

Guest (Customer)

[00:05:46] OK

Lauren R (Tutor)

[00:05:54] so how does that help us?

Guest (Customer)

[00:06:06] the cosines cross out

Lauren R (Tutor)

[00:06:12] yep and I am left with what?

[00:06:34] good

[00:06:40] we are SOOO CLOSE!!!

Guest (Customer)

[00:06:49] yay!

Lauren R (Tutor)

[00:07:11] ok, now the other thing I see here is cos squared and sine squared

[00:07:21] that brings to mind a specific identity

[00:07:30] sin ^2 + cos ^ 2 = 1

[00:07:36] does that one ring a bell?

Guest (Customer)

[00:07:49] yes it does

Lauren R (Tutor)

[00:08:02] ok, if you solve that for sin^2 what do you get?

[00:08:59] we dont have to do that

[00:09:05] just solve for sin, get rid of the cos

[00:10:13] you are on the right track

[00:11:06] look at wha tyou just found

[00:11:23] what does 1- cos ^ 2 euqal?

Guest (Customer)

[00:11:42] sin^2(theta)

Lauren R (Tutor)

[00:11:52] which is what it is supposed to equal right?

Guest (Customer)

[00:11:58] yes

Lauren R (Tutor)

[00:12:21] ok, this identity is HUGE

[00:12:32] sin ^2 + cos ^2 = 1 is used a lot

Guest (Customer)

[00:12:32] oh ok

Lauren R (Tutor)

[00:12:39] and its rearrangements are also used a lot

[00:12:48] sin^2 = 1-cos^2

[00:12:57] and cos^2 = 1-sin^2

[00:13:09] those are ones to keep handy since they do come up frequently

Guest (Customer)

[00:13:20] ok.I'll try ot remember those.

Lauren R (Tutor)

[00:13:34] they are good to remember if you have cosines and need to get to sines

[00:13:41] or vice versa

[00:14:24] The biggest thing with these is they are like puzzles, you have to play with them a bit and rearrange, think about one piece at a time and how you can change it to what you need

Guest (Customer)

[00:14:49] oh OK

Lauren R (Tutor)

[00:15:03] can I clarify anything with these type of problems?

Guest (Customer)

[00:15:31] I think I kind of got it now.

Lauren R (Tutor)

[00:15:52] remember you can always log back in with similar problems if you get stuck

Guest (Customer)

[00:16:33] OK.I'll log back in if need
anymore help.Thank you for
your help.I really appreciate
it.

Lauren R (Tutor)

[00:16:45] Thanks for using Tutor.com.Â Please fill out the survey as you leave so we can learn how we can better help you in the future!Â

Guest (Customer)

[00:16:57] bye

Lauren R (Tutor)

[00:17:02] bye