Verify the Identity sec(x)cot(x)=csc(x)

Problem

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

Solution

1. Rewrite the trigonometric functions on the left side in terms of sine and cosine using the reciprocal and quotient identities.

2. Substitute sec(x)=1/cos(x) and cot(x)=cos(x)/sin(x) into the expression.

sec(x)*cot(x)=1/cos(x)⋅cos(x)/sin(x)

3. Simplify the product by canceling the common factor of cos(x) in the numerator and denominator.

1/cos(x)⋅cos(x)/sin(x)=1/sin(x)

4. Apply the reciprocal identity 1/sin(x)=csc(x) to reach the right side of the identity.

1/sin(x)=csc(x)

Final Answer

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

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