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Math Help - Trigonometry Identities

  1. #1
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    Trigonometry Identities

    Hi I need help in proving trigonometric identities.

    The qn is Prove the identity:

    tan x/ 1 + cos x + tan x/1 - cos x = 2 (tan x + cot x )


    Thanks (;
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  2. #2
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    Quote Originally Posted by SniperMarksman View Post
    Hi I need help in proving trigonometric identities.

    The qn is Prove the identity:

    tan x/ 1 + cos x + tan x/1 - cos x = 2 (tan x + cot x )


    Thanks (;
    LHS = \frac{\tan x}{1 + \cos x} + \frac{\tan x}{1 - \cos x}

    = \frac{\tan x (1 - \cos x) + \tan x (1 + \cos x)}{(1 + \cos x) (1 - \cos x)}

    Numerator: Substitute \tan x = \frac{\sin x}{\cos x} and expand.

    Denominator: Note the (1 + \cos x) (1 - \cos x) = 1 - \cos^2 x = \sin^2 x.

    Continue simplifying until recognise that you've clearly got the RHS.
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  3. #3
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    O.o alright, thanks =D
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  4. #4
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    Thumbs up Angel (BestSolution)

    Still not proving..........please solve it completely please...............
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  5. #5
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    Quote Originally Posted by Angel View Post
    Still not proving..........please solve it completely please...............
    Excuse me??

    I have no intention of proving it. I've provided some direction for the OP.

    I will add however that the RHS is equivalent to \frac{2}{\cos x \sin x} ....
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  6. #6
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    Quote Originally Posted by Angel View Post
    Still not proving..........please solve it completely please...............
    You will please disist from automaticaly giving complete solutions, and not use the term "best solution" or its like in the titles of your posts.

    CB
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