Verify the Identity sec(x)*sin(x)*cot(x)=1

Problem

sec(x)*sin(x)*cot(x)=1

Solution

1. Express in terms of sine and cosine by using the reciprocal identity sec(x)=1/cos(x) and the quotient identity cot(x)=cos(x)/sin(x)

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

2. Multiply the fractions to combine the terms into a single expression.

(1⋅sin(x)⋅cos(x))/(cos(x)⋅sin(x))

3. Simplify the expression by canceling the common factors sin(x) and cos(x) from the numerator and the denominator.

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

Final Answer

sec(x)*sin(x)*cot(x)=1

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