Answer:
−1/cotθ
1/cot(−θ)
tan(−θ)
Step-by-step explanation:
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.
−1/cot(−θ)
tan θ
tan(−θ)----> tan(−θ) = −tan θ
