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    tth
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    Umm...?

    1. Although I suppose you could call a variable fetar, I think you're on about theta.
    2. What you've given isn't an equation, have you missed out an equality sign?
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    Dude youve missed out the what your trying to proove? And why does every insist on using same symbols just say 'x' instead of theta.
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    heyyy
    im sorry, clumsy mistake

    prove that : cot x cosec x / sec^2 x + cosec ^2 x = cos ^3 x


    thank you
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    (Original post by ash213)
    heyyy
    im sorry, clumsy mistake

    prove that : cot x cosec x / sec^2 x + cosec ^2 x = cos ^3 x
    cot x cosec x / sec^2 x + cosec ^2 x = cos ^3 x
    (1/tanx.1/sinx) / (1/cos²x + 1/sin²x) = cos³x
    (cosx/sinx.1/sinx) / (1/cos²x + 1/sin²x) = cos³x
    (cosx/sin²x) / ((sin²x + cos²x)/cos²xsin²x) = cos³x
    (cosx/sin²x) / (1/cos²xsin²x) = cos³x
    (cosx/sin²x).(cos²xsin²x) = cos³x
    (cos³xsin²x)/sin²x = cos³x

    the sine's cancel to leave...

    cos³x = cos³x
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    Damn Dekota that is fast. :cool:
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    (Original post by Dekota)
    cot x cosec x / sec^2 x + cosec ^2 x = cos ^3 x
    (1/tanx.1/sinx) / (1/cos²x + 1/sin²x) = cos³x
    (cosx/sinx.1/sinx) / (1/cos²x + 1/sin²x) = cos³x
    (cosx/sin²x) / ((sin²x + cos²x)/cos²xsin²x) = cos³x
    (cosx/sin²x) / (1/cos²xsin²x) = cos³x
    (cosx/sin²x).(cos²xsin²x) = cos³x
    (cos³xsin²x)/sin²x = cos³x

    the sine's cancel to leave...

    cos³x = cos³x
    When you are proving something you cannot just equate them. Start with LHS = whatever. Then simplify "whatever" until it is the RHS.
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    (Original post by samd)
    When you are proving something you cannot just equate them. Start with LHS = whatever. Then simplify "whatever" until it is the RHS.
    Err .. isn't this what I've done?
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    (Original post by Dekota)
    cot x cosec x / sec^2 x + cosec ^2 x = cos ^3 x
    (1/tanx.1/sinx) / (1/cos²x + 1/sin²x) = cos³x
    (cosx/sinx.1/sinx) / (1/cos²x + 1/sin²x) = cos³x
    (cosx/sin²x) / ((sin²x + cos²x)/cos²xsin²x) = cos³x
    (cosx/sin²x) / (1/cos²xsin²x) = cos³x
    (cosx/sin²x).(cos²xsin²x) = cos³x
    (cos³xsin²x)/sin²x = cos³x

    the sine's cancel to leave...

    cos³x = cos³x
    i agree with samd. You can't just let the expression equal the one you're trying to prove. It defeats the principle of proving it in the first place!
    You must express the expression in terms of sinx and cosx and simplify until you get the required expression. Then you can say LHS = RHS.
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    Fair enough; dear pedantic mathmos.
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    I love the instant change to patronising talk - the italics and 'dear' -

    Anyway, a slightly quicker way, (express everything in terms of coses and sines)

    (cos x/sin x)(1/sin x)
    =--------------
    (1/cos^2 x) + (1/sin^2 x)

    cos x
    =--------------
    (sin^2 x)((1/cos^2 x) + (1/sin^2 x))

    cos x
    =--------------
    tan^2 + 1

    cos x
    =--------------
    sec^2 x

    = cos^3 x.

    LHS=RHS
 
 
 

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