The tangent function is a the ratio for an angle defined as opposite / adjacent. A negative applied to −tan θ will give the opposite value. This is also true for the function when taken on a negative angle. tan(−θ) = −tan θ. This identity is also true for sin, sec, and cot. Recall that cotangent is the reciprocal of tangent and is defined as the ratio adjacent / opposite. Taking the reciprocal of cotangent will be the same as tangent. Using this information the following are equivalent:
1/cotθ
−1/cotθ ----> The reciprocal of Cot is Tan
1/cot(−θ)
----> The reciprocal of Cot is Tan and cot(−θ) = −cot θ.
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