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Math Help - trig equation and identity help.

  1. #1
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    trig equation and identity help.

    hi guys,

    i have a problem with this trig equation.


    1)5sinxcosx - sinx = 0

    i tried divding this equation with cos turing the equation in terms of tan to solve it , i got tan = 4, but the angles i got didn't match the answer of the book.

    2) tan(30 - x) = 2.
    in this equation i don't know how to manipulate the range. i know how to do it when you have for example(x - 30 degress),
    if say the range is -90 < x > 90
    do i just simple do 30-(-90) and 30-90 ?

    3) for the third question can someone prove this identity for me pls, i really have trouble proving it

    sinxtanx + cosx = secx


    thanks in advance
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  2. #2
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    Quote Originally Posted by llkkjj24 View Post
    hi guys,

    i have a problem with this trig equation.


    1)5sinxcosx - sinx = 0

    factor ...

    \textcolor{red}{\sin{x}(5\cos{x} - 1) = 0}

    set each factor equal to 0 and solve for x

    2) tan(30 - x) = 2.

    note that \textcolor{red}{\tan(-\theta) = -\tan{\theta}}

    3) for the third question can someone prove this identity for me pls, i really have trouble proving it

    sinxtanx + cosx = secx

    change tanx to sinx/cosx , get a common denominator, and add the two terms on the left side.
    ...
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