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

Problem

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

Solution

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

2. Express the secant function in terms of cosine using the reciprocal identity sec(x)=1/cos(x)

3. Substitute these identities into the left side of the equation.

cos(x)/sin(x)⋅1/cos(x)⋅sin(x)

4. Simplify the expression by canceling the common factors of cos(x) in the numerator and denominator.

1/sin(x)⋅sin(x)

5. Simplify the remaining expression by canceling the common factors of sin(x)

1

Final Answer

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

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