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March 26, 2017

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simplify the expression.


cos^2x+sin^2x/cot^2x-csc^2x

  • trig - ,

    Parentheses are assumed missing. Implied parentheses are ALWAYS required in numerator and denominator of fractions.

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

    This problem can be solved by converting all functions in terms of sine and cosine according to the standard definitions.

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

    Use sin²(u)+cos²(u)=1 to reduce the numerator to 1.
    Since the denominator has a common factor of sin²(x), we can simplify that too!

    =(1)/[(cos²(x)-1)/sin²(x)]
    =sin²(x)/(cos²(x)-1)
    =sin²(x)/(-sin²(x)
    =-1

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