Simplify tan(pi/2-x)tan(x)

Problem

tan(π/2−x)*tan(x)

Solution

1. Apply the cofunction identity for the tangent function, which states that tan(π/2−x)=cot(x)

tan(π/2−x)=cot(x)

2. Substitute the identity back into the original expression.

cot(x)*tan(x)

3. Use the reciprocal identity for the cotangent function, where cot(x)=1/tan(x)

1/tan(x)*tan(x)

4. Simplify the expression by canceling the common factor of tan(x)

1

Final Answer

tan(π/2−x)*tan(x)=1

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