Find the Exact Value tan(10)cot(10)

Problem

tan(10)*cot(10)

Solution

1. Identify the trigonometric identity for the cotangent function.

cot(θ)=1/tan(θ)

2. Substitute the identity into the original expression using θ=10

tan(10)⋅1/tan(10)

3. Simplify the expression by canceling the common factor of tan(10) in the numerator and denominator.

tan(10)/tan(10)=1

Final Answer

tan(10)*cot(10)=1

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