trig
posted by tony on .
simplify the expression.
cos^2x+sin^2x/cot^2xcsc^2x

Parentheses are assumed missing. Implied parentheses are ALWAYS required in numerator and denominator of fractions.
(cos^2x+sin^2x)/(cot^2xcsc^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^2xcsc^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