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Math Help - Prove the following identities.............

  1. #1
    Junior Member
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    Post Prove the following identities.............

    Prove the following identities:

    a) (cosec
    θ + cotθ)(cosecθ - cotθ) = cotθtanθ


    b) 2/(1 + sin
    θ) + 1/(1- sinθ) = (3sec^2)θ - tanθcosecθ


    I basically just have to prove Left HandSide = Right Hand Side
    *
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  2. #2
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    Hello, sweetG!

    Prove the following identities:

    a)\;\;\frac{\csc\theta + \cot\theta}{\csc\theta - \cot\theta} \:=\:\cot\theta\tan\theta . . . . This is not an identity

    b)\;\;\frac{2}{1 + \sin\theta} + \frac{1}{1-\sin\theta} \:=\:3\sec^2\!\theta - \tan\theta\,{\color{red}\csc\theta\;\;?}

    Combine the fractions:

    \frac{2}{1+\sin\theta}\!\cdot\!{\color{blue}\frac{  1-\sin\theta}{1-\sin\theta}} + \frac{1}{1-\sin\theta}\!\cdot\!{\color{blue}\frac{1+\sin\thet  a}{1+\sin\theta}} \;\;=\;\;\frac{2(1-\sin\theta) + (1+\sin\theta)}{(1+\sin\theta)(1-\sin\theta)}

    . . = \;\;\frac{3-\sin\theta}{1-\sin^2\!\theta} \;\;=\;\;\frac{3-\sin\theta}{\cos^2\!\theta} \;\;=\;\;\frac{3}{\cos^2\!\theta} - \frac{\sin\theta}{\cos^2\!\theta}

    . . = \;\;3\!\cdot\!\frac{1}{\cos^2\!\theta} - \frac{\sin\theta}{\cos\theta}\!\cdot\!\frac{1}{\co  s\theta} \;\;=\;\;3\sec^2\!\theta - \tan\theta\,{\color{red}\sec\theta}

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