Simplify sec(-x)cot(x)

Problem

sec(−x)*cot(x)

Solution

1. Apply the even-odd identity for the secant function, which states that sec(−x)=sec(x)

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

3. Substitute these expressions into the product:

1/cos(x)⋅cos(x)/sin(x)

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

5. Simplify the remaining expression 1/sin(x) using the cosecant identity csc(x)=1/sin(x)

Final Answer

sec(−x)*cot(x)=csc(x)

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