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Math Help - help on proving trig identity

  1. #1
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    Question help on proving trig identity

    prove the following identity:

    Secθ- 1/ Secθ +1 ≡ Tan θ/2 (only the theta is divided by 2)

    this is what i've done so far:

    LHS =( secθ- 1)/ (secθ +1)

    = (1/cosθ - 1) /(1/cosθ +1 )

    = 1- cosθ/ 1+ cosθ

    from here, I don't know what to do next. help plz!!!
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  2. #2
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    Hello ladythugette
    Quote Originally Posted by ladythugette View Post
    prove the following identity:

    Secθ- 1/ Secθ +1 ≡ Tan θ/2 (only the theta is divided by 2)

    this is what i've done so far:

    LHS =( secθ- 1)/ (secθ +1)

    = (1/cosθ - 1) /(1/cosθ +1 )

    = 1- cosθ/ 1+ cosθ

    from here, I don't know what to do next. help plz!!!
    You're doing great so far!

    Now use
    \cos\theta = 1-2\sin^2(\tfrac12\theta)
    on the top, and
    \cos\theta = 2 \cos^2(\tfrac12\theta)-1
    on the bottom, and you're there!

    Grandad
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  3. #3
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    Quote Originally Posted by Grandad View Post
    Hello ladythugetteYou're doing great so far!

    Now use
    \cos\theta = 1-2\sin^2(\tfrac12\theta)
    on the top, and
    \cos\theta = 2 \cos^2(\tfrac12\theta)-1
    on the bottom, and you're there!

    Grandad
    oh wow thanks!!!.. i'm definitely going to remember those two equations before my exam. i keep thinking that cosθ can not be changed unless there is a number infront of θ, then i'd know to use the double angle formulae for cos
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  4. #4
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    Quote Originally Posted by ladythugette View Post
    oh wow thanks!!!.. i'm definitely going to remember those two equations before my exam. i keep thinking that cosθ can not be changed unless there is a number infront of θ, then i'd know to use the double angle formulae for cos
    Grandad did use the double angle formula

    cos(\theta) = cos\left(\frac{\theta}{2} + \frac{\theta}{2}\right) = cos \left(2\, \frac{\theta}{2}\right)
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