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Math Help - [SOLVED] Trig Identity proofs

  1. #1
    raveen4706
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    [SOLVED] Trig Identity proofs

    Could someone please prove secx - 1/ 1 - cos x = sec x and 1/ tanx + cotx = sinxcosx?

    x = angle
    Thanks in advance
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  2. #2
    Super Member

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    Hello, raveen4706!

    You really must learn to use parentheses . . .


    \frac{\sec x - 1}{1 - \cos x}\; =\;\sec x
    The left side is: . \frac{\frac{1}{\cos x} - 1}{1 - \cos x}

    Multiply top and bottom by \cos x\!:\;\;\frac{\cos x}{\cos x}\cdot\frac{\frac{1}{\cos x} - 1}{1 - \cos x} \;=\;\frac{1 - \cos x}{\cos x(1 - \cos x)}

    Reduce: . \frac{1}{\cos x} \;=\;\sec x



    \frac{1}{\tan x + \cot x} \:= \:\sin x\cos x

    The left side is: . \frac{1}{\frac{\sin x}{\cos x} + \frac{\cos x}{\sin x}}

    Multiply top and bottom by \sin x\cos x\!:\;\;\frac{\sin x\cos x}{\sin x\cos x}\cdot\frac{1}{\frac{\sin x}{\cos x} + \frac{\cos x}{\sin x}}

    And we get: . \frac{\sin x\cos x}{\sin^2\!x + \cos^2\!x} \;=\;\frac{\sin x\cos x}{1} \;=\;\sin x\cos x

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