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March 28, 2015

Posted by **tony** on Sunday, July 14, 2013 at 6:22pm.

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

- trig -
**MathMate**, Sunday, July 14, 2013 at 7:21pmParentheses 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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