Question #348ea

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Answer 1 · 2017-03-02T22:31:00

see below

Use the Reciprocal Property

$cot v = \frac{1}{tan v} or tan v = \frac{1}{cot v}$ $cot v=1/tanv or tan v=1/cotv$

Left Hand Side:

$\frac{1 + tan v}{1 - tan v} = \frac{1 + \frac{1}{cot v}}{1 - \frac{1}{cot v}}$ $(1+tan v)/(1-tan v) =( 1+1/cot v)/(1-1/cot v)$

$= \frac{\frac{cot v}{cot v} + \frac{1}{cot v}}{\frac{cot v}{cot v} - \frac{1}{cot v}}$ $=(cot v/cotv +1/cot v)/(cot v/cot v-1/cot v)$

$= \frac{\frac{cot v + 1}{cot v}}{\frac{cot v - 1}{cot v}}$ $=((cotv+1)/cotv)/((cotv-1)/cotv)$

$= \frac{cot v + 1}{cot v} \cdot \frac{cot v}{cot v - 1}$ $=(cotv+1)/cotv * cot v/(cot v-1)$

$=(cotv+1)/cancelcotv * cancelcot v/(cot v-1)$

$=(cot v+1)/(cot v-1)$

$:.=$ Right Hand Side