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Math Help - Trig Proof (+more)... VERY QUICKK PLEASE

  1. #1
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    Exclamation Trig Proof (+more)... VERY QUICKK PLEASE

    help!!

    prove....
    secX-tanX= 1/(secX+tanX)

    then deduce that

    0<secX - tanX <(or equal to) 1
    for values of x between 0 and pi/2

    fianlly..
    given that secX- tanX = 1/2

    find exact value of X

    thanks
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  2. #2
    Super Member angel.white's Avatar
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    Quote Originally Posted by pook View Post
    help!!

    prove....
    secX-tanX= 1/(secX+tanX)
    sec~x-tan~x= \frac 1{sec~x+tan~x}

    sec~x-tan~x= \frac 1{\frac 1{cos~x}+\frac {sin~x}{cos~x}}

    sec~x-tan~x= \frac 1{\frac {1+sin~x}{cos~x}}

    sec~x-tan~x= \frac {cos~x}{1+sin~x}

    sec~x-tan~x= \frac {cos~x}{1+sin~x}*\frac{1-sin~x}{1-sin~x}

    sec~x-tan~x= \frac {cos~x-cos~x~sin~x}{1-sin^2~x}

    sec~x-tan~x= \frac {cos~x-cos~x~sin~x}{cos^2~x}

    sec~x-tan~x= \frac {cos~x}{cos^2~x}-\frac{cos~x~sin~x}{cos^2~x}

    sec~x-tan~x= \frac {1}{cos~x}-\frac{sin~x}{cos~x}

    sec~x-tan~x= sec~x-tan~x
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  3. #3
    Member Jonboy's Avatar
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    i can help with your first question.

    sec\,x - tan\,x = \frac{1}{sec\,x + tan\,x}

    Multiply both sides by sec\,x + tan\,x:

    sec^2\,x - tan^2\,x = 1

    There's an identity: 1 + tan^2\,x = sec^2\,x

    Re-arrange that to: sec^2\,x - tan^2\,x = 1

    Thus the left side side of sec^2\,x - tan^2\,x = 1 becomes one and the proof is complete.
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