Simplifying with Trigonometry Identities

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/1-Sinx - 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/(1-sinx) - tanx =

cosx/(1-sinx) - sinx/cosx =

Common denominator is: (1-sinx)(cosx)

Therefore:
cos^2x/(1-sinx)(cosx) - sinx(1-sinx)/(1-sinx)(cosx) =

[cos^2x - (sinx - sin^2x)]/(1-sinx)(cosx) =

(cos^2x + sin^2x - sinx)/(1-sinx)(cosx) =

(1 - sinx)/(1-sinx)(cosx) =

1/cosx =

secx = secx

I hope this helps with this one; perhaps someone else can help with the first problem.

  1. 👍 0
  2. 👎 0
  3. 👁 258
asked by amanda
  1. (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

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Studying

    Hey guys, I would appreciate it if y'all took some time to answer this for me. Thanks ahead of time!! I am involved in many difficult High School courses, and I also am a team member of the school academic team, and I was

    asked by LR on November 14, 2017
  2. Math

    A high school senior vacationing in Jamaica for her senior class trip jumped off a 20 foot cliff into a pool of water. The height of the senior above the water is modeled by the function h(t)=-t^2+t/4+5/4 where h(t) is the height

    asked by Anonymous on February 13, 2014
  3. English

    1. I am a freshman in high school. 2. I am a freshman of high school. (Which preposition should we use? Are both OK?) 3. There'll be a parade on the anniversary day. (How do you pronounce "There'll"?) 4. We'll choose between upper

    asked by rfvv on March 8, 2011
  4. proofread

    Can someone please proofread this before i email it to school metro's director Mr. Thomas LeMera Hey LeMera, my name is Bryan Martin and I’m email you to require more information on your school. I am a senior in high school in

    asked by Bryan on October 23, 2007
  5. College Help

    I am a Sophomore in High School. I have a GPA of 3.3 currently, (it's very bad) with no AP classes taken until Junior and Senior year. What are my chances of getting into UC Irvine? That's the school I really want to get into!

    asked by William on April 16, 2011
  6. Math

    Nathaniel school is selling tickets to a spring Musical on the first day of ticket sales the school so 3 senior citizen tickets and nine children tickets to for a total of $75 the school took in $67 on the school on the second day

    asked by Naseem on April 2, 2016
  7. English

    An upper-secondary school is a senior high school. Then is a lower-secondary school a junior high school? Where is the expression 'a lower-secondary school' used?

    asked by rfvv on February 8, 2015
  8. English

    Help:Please change show me anthing that I need to do, by placing the correct form at the it the bottom of the essay. Topic: What is your biggest regret in life? My Biggest Regret Everyone has had some regrets about something in

    asked by Angel on November 10, 2009
  9. Algebra

    Help? The school john goes to is selling tickets to the annual dance competition . On the first day of sales the school sold 2 senior citizen tickets and 13 student tickets for a total of $108. The school took in$144 on the second

    asked by Teagan on October 20, 2014
  10. ENGLISH

    Help:Please change show me anthing that I need to do, by placing the correct form at the it the bottom of the essay. Topic: What is your biggest regret in life? My Biggest Regret Everyone has had regrets about something in life.

    asked by Angel on November 12, 2009

More Similar Questions