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Math Help - HELP! Trig-Proving Identities

  1. #1
    BabaCA07
    Guest

    HELP! Trig-Proving Identities

    I'm having trouble proving this problem:

    sec+cot/sec=1+csc-sin

    Please help!
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  2. #2
    TD!
    TD! is offline
    Senior Member
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    3
    1) Don't post your problem twice.
    2) There is no such thing as "sin", the argument is missing.
    3) Don't forget brackets, your expression is wrong now.

    Now, let's see

    <br />
\frac{{\sec x + \cot x}}{{\sec x}} = 1 + \frac{{\cot x}}{{\sec x}} = 1 + \frac{{\frac{{\cos x}}{{\sin x}}}}{{\frac{1}{{\cos x}}}} = 1 + \frac{{\cos ^2 x}}{{\sin x}}<br />

    <br />
1 + \frac{{\cos ^2 x}}{{\sin x}} = 1 + \frac{{1 - \sin ^2 x}}{{\sin x}} = 1 + \frac{1}{{\sin x}} - \sin x<br />

    Since 1/sin(x) = csc(x), we have what we wanted: LHS = RHS.
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