Results 1 to 2 of 2

Math Help - Help to prove each Identity

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    1

    Help to prove each Identity

    I have no idea how to solve these problems, any help wold be aprreciated

    a) tanθ - 1 = (sin^2θ - cos^2θ) / (sinθcosθ + cos^2θ)

    b) sinx + sinxcot^2x = cscx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,710
    Thanks
    629
    Hello, AdamEdward!

    (a)\;\;\tan\theta - 1 \:=\: \frac{\sin^2\!\theta - \cos^2\!\theta}{\sin\theta\cos\theta + \cos^2\!\theta}

    Factor the right side: . \frac{(\sin\theta - \cos\theta)(\sin\theta + \cos\theta)}{\cos\theta(\sin\theta + \cos\theta)}

    Reduce: . \frac{\sin\theta - \cos\theta}{\cos\theta} \;\;=\;\;\frac{\sin\theta}{\cos\theta} - \frac{\cos\theta}{\cos\theta} \;\;=\;\; \tan\theta - 1




    (b)\;\;\sin x + \sin x\cot^2\!x \:=\: \csc x

    Factor the left side: . \sin x\cdot\underbrace{(1 + \cot^2\!x)}_{\text{This is }\csc^2\!x} \;\;=\;\;\sin x\cdot\csc^2\!x \;\;=\;\;\frac{1}{\csc x}\!\cdot \csc^2\!x \;\;=\;\;\csc x

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. prove identity help!
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: December 2nd 2010, 10:00 AM
  2. prove the identity
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 7th 2010, 05:03 PM
  3. Prove this identity?
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: April 5th 2010, 05:29 PM
  4. Prove that each of the following is an identity
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 18th 2009, 02:39 PM
  5. Prove the Identity
    Posted in the Trigonometry Forum
    Replies: 10
    Last Post: February 25th 2008, 05:29 PM

Search Tags


/mathhelpforum @mathhelpforum