Simplify sec(x)^2cot(x)^2

Problem

sec(x)*cot(x)

Solution

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

sec(x)*cot(x)=(1/cos(x))2*(cos(x)/sin(x))2

2. Apply the exponent to the numerators and denominators.

1/cos(x)⋅cos(x)/sin(x)

3. Cancel the common factor of cos(x) from the numerator and the denominator.

1/sin(x)

4. Identify the reciprocal identity csc(x)=1/sin(x) to simplify the expression further.

csc(x)

Final Answer

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

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