Proving trigonometry identities

Posted on 2006-04-03
Last Modified: 2009-12-16
Prove that   1  over 1-cosx   -      1 over 1+cosx  =   2cotxcscx
Question by:jkk11
    LVL 84

    Accepted Solution

    1 /( 1-cosx)   -  1/( 1+cosx)
    = (1+cosx)/((1+cosx)*(1-cosx)) - (1-cosx)/((1-cosx)*(1+cosx))
    LVL 37

    Assisted Solution

    by:Harisha M G

    1 /( 1-cosx)   -  1/( 1+cosx)
    = (1 + cos x - 1 + cos x) / (1 - cos² x)
    = 2cos x/sin² x
    = 2(cos x/(sin x*sin x)
    = 2(cos x/sin x)/sin x
    = 2 tan x csc x

    LVL 27

    Assisted Solution

    1 /( 1-cosx)   -  1/( 1+cosx)


    (1+cosx) - (1-cosx) all divided by (1-cosx)(1+cosx)

    The numerator is 2cosx, the denominator 1-cos²x = sin²x

    as cosx/sinx is cotx and 1/sinx is cscx, we get 2cotxcscx.


    Quite Easily Done.

    BTW: This question is NOT worth 500 points. It looks anyway like home work and ought to be reduce to 50 points.

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