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Math Help - Prove Identities

  1. #1
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    Prove Identities

    hi,
    can u help me?
    I have spent over 2 hours trying to figure it out but was unsucessful. can you please prove the identities. thanks!
    1) Cos X/Sec X - 1 - Cos X/tan^2 X = Cot^2 X

    2) Sin X / 1 - Cos X + 1 - Cos X / Sin X = 2CSC X
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  2. #2
    MHF Contributor
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    Quote Originally Posted by satishgaire View Post
    hi,
    can u help me?
    I have spent over 2 hours trying to figure it out but was unsucessful. can you please prove the identities. thanks!
    1) Cos X/Sec X - 1 - Cos X/tan^2 X = Cot^2 X

    2) Sin X / 1 - Cos X + 1 - Cos X / Sin X = 2CSC X
    hi

    (1) Combine the fractions first to get .

    \frac{\sin^2 x+(1-\cos x)^2}{\sin x(1-\cos x)}

    \frac{\sin^2 x+\cos^2 x+1-2\cos x}{\sin x(1-\cos x)}

    try continuing here .

    (2) \frac{\cos x}{\sec x-1}\cdot \frac{\sec x+1}{\sec x+1}-\frac{\cos x}{\tan^2 x}

    \frac{\cos x\sec x+\cos x}{\sec^2 x-1 }-\frac{\cos x}{\tan^2 x}

    \frac{1+\cos x}{\tan^2 x}-\frac{\cos x}{\tan^2 x}

    Then simplify .
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