Rewrite cot(^2)xcosx/(cscx-1) as an expression that doesn't involve a fraction.
To rewrite the expression cot^2(x)cos(x)/(csc(x)-1) without fractions, we can use the reciprocal identities and rewrite them in terms of sine and cosine.
Recall the reciprocal identities:
cot(x) = 1/tan(x)
csc(x) = 1/sin(x)
Using these identities, we can transform the expression step by step:
1. Start with cot^2(x)cos(x)/(csc(x)-1)
2. Substitute cot(x) with 1/tan(x) and csc(x) with 1/sin(x): (1/tan(x))^2cos(x)/(1/sin(x) - 1)
3. Simplify the square of the cotangent: (1/tan^2(x))cos(x)/(1/sin(x) - 1)
4. Rewrite tangent in terms of sine and cosine: (cos^2(x)/sin^2(x))cos(x)/(1/sin(x) - 1)
5. Multiply the numerators: cos^3(x)/(sin^2(x)(1/sin(x) - 1))
6. Distribute sin(x) to the denominator: cos^3(x)/(sin(x)/sin^2(x) - sin(x))
7. Simplify the denominator: cos^3(x)/(1/sin(x) - sin(x))
8. Multiply the numerator and denominator by sin(x) to eliminate the fraction in the denominator:
cos^3(x)sin(x)/(1 - sin^2(x))
Therefore, the expression cot^2(x)cos(x)/(csc(x)-1) can be rewritten as cos^3(x)sin(x)/(1 - sin^2(x)), where no fractions are involved.