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Math Help - Proving identities

  1. #1
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    Proving identities

    hello, i am having problems with my homework, theres five problems i can not figure out, any help would be great,

    1) cot x * sec x * sin x = 1


    2) 2sec^2 y =1/(1 - sin y) + 1/(1 + sin y)


    3) sec^2 a + csc^2 a = sec^2 a * csc^2 a


    4) sin^4 β - cos^4 β = 1 - 2cos^2 β

    5) cos Φ/(1 + sinΦ) + (1 + sin Φ)/cos Φ = 2sec Φ


    HELP PLEASEE!!!!!!!!!!!
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by jpenny32 View Post
    hello, i am having problems with my homework, theres five problems i can not figure out, any help would be great,

    1) cot x * sec x * sin x = 1


    2) 2sec^2 y =1/(1 - sin y) + 1/(1 + sin y)


    3) sec^2 a + csc^2 a = sec^2 a * csc^2 a


    4) sin^4 β - cos^4 β = 1 - 2cos^2 β

    5) cos Φ/(1 + sinΦ) + (1 + sin Φ)/cos Φ = 2sec Φ


    HELP PLEASEE!!!!!!!!!!!
    1) L.H.S. = cot x \times sec x \times sin x = \frac{cosx}{sinx} \times \frac{1}{cosx} \times sinx = 1

    2) R.H.S = \frac{1}{1-siny} + \frac{1}{1+siny} = \frac{(1+siny)+(1-siny)}{(1-siny)(1+siny)}
    = \frac{2}{(1-sin^{2}y)}= \frac{2}{cos^{2}y} = 2sec^{2}y

    3) L.H.S. = sec^{2}a + csc^{2}a = \frac{1}{cos^{2}a} + \frac{1}{sin^{2}a} = \frac{sin^{2}a + cos^{2}a}{cos^{2}a \times sin^{2}a}
    = \frac{1}{cos^{2}a \times sin^{2}a} = \frac{1}{cos^{2}a } \times \frac{1}{sin^{2}a} = sec^{2}a \times csc^{2}a



    Similarly, try using trigonometric identities on the other 2 questions.
    Last edited by harish21; April 4th 2010 at 08:29 PM.
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