Check the solution to "Establish identity csc⁡v−1csc⁡v+1=1−sin⁡v1+sin⁡v"

Cabiolab

Answered question

2021-09-01

Establish identity

\frac{\csc v - 1}{\csc v + 1} = \frac{1 - \sin v}{1 + \sin v}

funblogC

Skilled2021-09-02Added 91 answers

Given identity

\frac{\csc v - 1}{\csc v + 1} = \frac{1 - \sin v}{1 + \sin v}

First from the left-hand side,

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

Here use the trigonometry reciprocal identity,

\csc θ = \frac{1}{\sin θ}

\frac{\csc v - 1}{\csc v + 1} = \frac{\frac{1}{\sin v} - 1}{\frac{1}{\sin v} + 1}

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

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

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

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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