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Math Help - Using Basic identities to simply the expression

  1. #1
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    Using Basic identities to simply the expression

    Problem:

    cos^2(x) / sin^2(x) + csc(x)sin(x)


    I've worked on it,
    On the right of the + sign I changed the csc(x) into 1/sin(x)
    so...
    cos^2(x) / (sin^2(x)) + 1/sin(x) * sin(x)
    cos^2(x) / (sin^2(x)) + 1
    1/sec^2(x) / (sin^2(x)) +1
    1/sec^2(x) / (1/ csc^2(x)) + 1

    then i dont know where to go from there...
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by yeunju View Post
    Problem:

    cos^2(x) / sin^2(x) + csc(x)sin(x)


    I've worked on it,
    On the right of the + sign I changed the csc(x) into 1/sin(x)
    so...
    cos^2(x) / (sin^2(x)) + 1/sin(x) * sin(x)
    cos^2(x) / (sin^2(x)) + 1
    1/sec^2(x) / (sin^2(x)) +1
    1/sec^2(x) / (1/ csc^2(x)) + 1

    then i dont know where to go from there...
    Hi yeunju,

    Here's what I did:

    \frac{\cos^2 x}{\sin^2 x}+\csc x \sin x

    \frac{\cos^2 x}{\sin^2 x}+\frac{1}{\sin x}(\sin x)

    \frac{\cos^2 x}{\sin^2 x}+1

    \frac{\cos^2 x+ \sin^2 x}{\sin^2 x}

    \frac{1}{\sin^2 x}

    \csc^2 x
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