Q:

Which expressions are equivalent to −tan⁡ θ?There may be more than one correct answer. Select all that apply. 1/cotθ −1/cotθ 1/cot(−θ) −1/cot(−θ) tan/ θ tan/(−θ)

Accepted Solution

A:
Answer:−1/cotθ1/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 Tan1/cot(−θ) ----> The reciprocal of Cot is Tan and cot(−θ) = −cot⁡ θ.−1/cot(−θ) tan θ tan(−θ)----> tan(−θ) = −tan⁡ θ