Simplify (csc(x)^2)/(cot(x))

Problem

csc2(x)/cot(x)

Solution

1. Rewrite the trigonometric functions in terms of sine and cosine using the identities csc(x)=1/sin(x) and cot(x)=cos(x)/sin(x)

csc2(x)/cot(x)=((1/sin(x))2)/cos(x)/sin(x)

2. Simplify the numerator by squaring the fraction.

1/sin2(x)/cos(x)/sin(x)

3. Multiply the numerator by the reciprocal of the denominator to simplify the complex fraction.

1/sin2(x)⋅sin(x)/cos(x)

4. Cancel the common factor of sin(x) from the numerator and the denominator.

1/(sin(x)*cos(x))

5. Apply reciprocal identities to express the result in terms of cosecant and secant.

1/sin(x)⋅1/cos(x)=csc(x)*sec(x)

Final Answer

csc2(x)/cot(x)=csc(x)*sec(x)

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