Solved: "Establish identity 1+tan⁡v1−tan⁡v=cot⁡v+1cot⁡v−1"

texelaare

Answered question

2021-09-12

Establish identity

\frac{1 + \tan v}{1 - \tan v} = \frac{\cot v + 1}{\cot v - 1}

hesgidiauE

Skilled2021-09-13Added 106 answers

Given identity

\frac{1 + \tan v}{1 - \tan v} = \frac{\cot v + 1}{\cot v - 1}

First from the left-hand side,

\frac{1 + \tan v}{1 - \tan v}

Here use the trigonometry reciprocal identity,

\tan θ = \frac{1}{\cot θ}

\frac{1 + \tan v}{1 - \tan v} = \frac{1 + \frac{1}{\cot v}}{1 - \frac{1}{\cot v}}

= \frac{\frac{\cot v + 1}{\cot v}}{\frac{\cot v - 1}{\cot v}}

= \frac{\cot v + 1}{\cot v - 1}

Therefore it is established that the left-hand side equal to the right-hand side quantity.

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