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    I've been struggling with this question, can someone please help.

    The question is to prove the identity:
    (sec^2x + tan^2x)(cosec^2x + cot^2x) = 1+ 2sec^2xcosec^2x


    btw sec^2x means sec squared x idk if i wrote that clearly.

    Anyway, the hint given on the sheet is to replace both tan squared x and cot squared x with identities and expand the brackets.

    I did that and I got
    (2sec^2x -1)(2cosec^2x -1)

    and when expanded that is
    4cosec^2xsec^2x -2sec^2x - 2cosec^2x +1


    but I dont know if thats wrong or right, and if it is right how would I equate that to 1 + 2sec^2xcosec^2x


    Please help me out, thanks
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    (Original post by _s_ox)
    I've been struggling with this question, can someone please help.

    The question is to prove the identity:
    (sec^2x + tan^2x)(cosec^2x + cot^2x) = 1+ 2sec^2xcosec^2x


    btw sec^2x means sec squared x idk if i wrote that clearly.

    Anyway, the hint given on the sheet is to replace both tan squared x and cot squared x with identities and expand the brackets.

    I did that and I got
    (2sec^2x -1)(2cosec^2x -1)

    and when expanded that is
    4cosec^2xsec^2x -2sec^2x - 2cosec^2x +1


    but I dont know if thats wrong or right, and if it is right how would I equate that to 1 + 2sec^2xcosec^2x


    Please help me out, thanks
    It's right; try writing the bit I've bolded in terms of sine and cosine (i.e using secx = 1/cosx, cosecx = 1/sinx), and go from there.
 
 
 
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