Simplifying with Trigonometry Identities
posted by amanda on .
Hi, I am a senior in High School having a really difficult time with two problems. I have to prove using the trigonometric identities that they equal each other but I am having a really hard time trying to get them to equal each other. I've spent over 2 hours trying to get these two problems right but I can't. I don't know if the math problems themselves are working because there is some error or that I am just doing them wrong (even though I've spent a long time trying various methods to get them correct). So I was wondering if someone could help me really soon. Here are the problems:
Thank you so much!
1: (1+Cotx)^2/Tanx = CosxCsc^3x + 2Cot^2x
2: Cosx/1Sinx  Tanx = Secx
#2:
Here are some basic trig identities to help with this problem.
sin^2x + cos^2x = 1
secx = 1/cosx
tanx = sinx/cosx
Let's try to get the left side to look like the right side.
cosx/(1sinx)  tanx =
cosx/(1sinx)  sinx/cosx =
Common denominator is: (1sinx)(cosx)
Therefore:
cos^2x/(1sinx)(cosx)  sinx(1sinx)/(1sinx)(cosx) =
[cos^2x  (sinx  sin^2x)]/(1sinx)(cosx) =
(cos^2x + sin^2x  sinx)/(1sinx)(cosx) =
(1  sinx)/(1sinx)(cosx) =
1/cosx =
secx = secx
I hope this helps with this one; perhaps someone else can help with the first problem.

(1+cotx)^2/tanx
=(1+2cotx+cot^2x)/(sinx/cosx)
=[(1+cot^2x)+2cotx]/(sinx/cosx)
=csc^2x/(sinx/cosx)+2cotx/(sinx/cosx)
=csc^2xcosx/(1/sinx)+2cotxcosx/sinx
=csc63xcosx+2cot^2x