Simplify (tan(theta))/(cot(theta))

Problem

tan(θ)/cot(θ)

Solution

1. Use trigonometric identities to rewrite the denominator in terms of the numerator. Recall that cot(θ)=1/tan(θ)

2. Substitute the identity into the original expression:

tan(θ)/1/tan(θ)

3. Simplify the fraction by multiplying the numerator by the reciprocal of the denominator:

tan(θ)⋅tan(θ)

4. Apply the exponent rule to combine the terms:

tan2(θ)

Final Answer

tan(θ)/cot(θ)=tan2(θ)

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