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    Hi all,

    Can someone help me with proving the following please? I have got to a certain point, but I am not sure after that.

    (sec^2 x)/(sec x +1)(sec x - 1) = cosec^2 x

    Thank you!
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    I'd always approach these problems by expanding anything that looks promising. You can expand out (sec x + 1)(sec x - 1) to give you a more familiar trigonometric identity.

    Just remember that you can rearrange tan^2 x + 1 = sec^2 x and you'll be fine.
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    (Original post by londoncricket)
    Hi all,

    Can someone help me with proving the following please? I have got to a certain point, but I am not sure after that.

    (sec^2 x)/(sec x +1)(sec x - 1) = cosec^2 x

    Thank you!
    What have you done so far?
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    (Original post by londoncricket)
    Hi all,

    Can someone help me with proving the following please? I have got to a certain point, but I am not sure after that.

    (sec^2 x)/(sec x +1)(sec x - 1) = cosec^2 x

    Thank you!
    Hope this helps
    (1)expand denominator to give sec2x/sec2x-1
    (2)Recall that sin2x+cos2x=1, divide through by cos2x.
    (3)Which gives tan2x+1=sec2x => tan2x=sec2x-1
    (4)Replace denominator in (1) with tan2x
    (5) This gives sec2x/tan2x => (1/cos2x) / (sin2x/cos2x)
    (6) This gives cos2x/cos2xsin2x
    (7) cancel cos2x terms to give 1/sin2x
    (8) 1/sin2x = cosec2x which equals RHS
 
 
 
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