Results 1 to 7 of 7

Math Help - Prove the IDENTITY

  1. #1
    Junior Member
    Joined
    Mar 2008
    Posts
    35

    Question Prove the IDENTITY

    1+tan^2 x/tan^2 x = csc^2 X

    I tried to prove this identity and I couldn't plz help Thanks...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    Quote Originally Posted by victorfk06 View Post
    1+tan^2x/tan^2x = csc^2 X

    I tried to prove this identity and I couldn't plz help Thanks...
    Transform \tan^2x=\frac{\sin^2x}{\cos^2x}

    -->
    \begin{aligned} \frac{1+tan^2x}{tan^2x} &=\frac{1+\frac{\sin^2x}{\cos^2x}}{\frac{\sin^2x}{  \cos^2x}} \\<br />
&=\left(1+\frac{\sin^2x}{\cos^2x}\right) \cdot \frac{\cos^2x}{\sin^2x} \\<br />
&=\left(\cos^2x+\sin^2x\right) \cdot \frac{1}{\sin^2x} \\<br />
&=\dots \end{aligned}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2008
    Posts
    35
    Then what I didn't understand it?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Quote Originally Posted by victorfk06 View Post
    Then what I didn't understand it?
    Erm... pardon me , but are you saying you wonder why you didn't see it, or that you still don't understand it ?

    Here's a tip, for the future :

    You're with a tan function, and you want to get to sines (csc is just 1/sin). So one of the ways (it depends on the situation) is to remember that the relation between tan and sin is :

    tan=sin/cos

    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Mar 2008
    Posts
    35
    Oh thanks dats the final answer correct?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    I'm confused lol !



    What follows my expressions is :

    \begin{aligned} \dots &=(\sin^2x+\cos^2x) \cdot \frac{1}{\sin^2x} \\<br />
&=1 \cdot \frac{1}{\sin^2x} \\<br />
&=\left(\frac{1}{\sin x}\right)^2 \\<br />
&=csc^2 x \end{aligned}
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,547
    Thanks
    539
    Hello, victorfk06!

    We're expected to know some basic identities . . .


    Prove: . \frac{1+\tan^2\!x}{\tan^2\!x}\:= \:\csc^2\!x

    \text{We have: }\;\overbrace{\frac{1}{\tan^2\!x}}^{\text{This is }\cot^2\!x} + \frac{\tan^2\!x}{\tan^2\!x} \;\;=\;\;\underbrace{\cot^2\!x + 1}_{\text{This is }\csc^2\!x} \;\;=\;\;\csc^2\!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