How do you verify $\frac{1 + tan x}{1 + cot x} = 2$ $(1+tan x) / (1+cot x) = 2$ ?

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How do you verify $\frac{1 + tan x}{1 + cot x} = 2$ $(1+tan x) / (1+cot x) = 2$ ?

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Answer 1 · 2015-06-18T02:47:31

It is not possible to verify #(1+tan(x))/(1+cot(x)) = 2
because it isn't (in general) true.

Explanation:

As an obvious counter example consider the case when $x = \frac{π}{4}$ $x=pi/4$ .

$XXXX$ $color(white)("XXXX")$ $\frac{1 + tan (\frac{π}{4})}{1 + cot (\frac{π}{4})}$ $(1+tan(pi/4))/(1+cot(pi/4))$

$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ $= \frac{1 + 1}{1 + 1}$ $=(1+1)/(1+1)$

$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ $= 1$ $= 1$

$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ $\neq 2$ $!= 2$

In fact with very little manipulation it is easy to show:
$XXXX$ $color(white)("XXXX")$ $\frac{1 + tan (x)}{1 + cot (x)} = tan (x)$ $(1+tan(x))/(1+cot(x)) = tan(x)$

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How do you verify $\frac{1 + tan x}{1 + cot x} = 2$ $(1+tan x) / (1+cot x) = 2$ ?

1 Answer

Explanation:

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How do you verify (1+tan x) / (1+cot x) = 21+tanx1+cotx=2(1+tan x) / (1+cot x) = 2?

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How do you verify $\frac{1 + tan x}{1 + cot x} = 2$ $(1+tan x) / (1+cot x) = 2$ ?