How do you prove the identity $tan 2 X cot X = 3$ $tan2XcotX=3$ ?

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How do you prove the identity $tan 2 X cot X = 3$ $tan2XcotX=3$ ?

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Answer 1 · 2015-10-07T10:45:19

It isn't.

Explanation:

$tan (2 x) \cdot cot (x) = 3$ $tan(2x)*cot(x) = 3$

Using the double angle formula,

$\frac{2 tan (x)}{1 - {tan}^{2} (x)} \cdot cot (x) = 3$ $(2tan(x))/(1-tan^2(x))*cot(x) = 3$

Knowing that $tan (x) \cdot cot (x) = 1$ $tan(x)*cot(x) = 1$

$\frac{2}{1 - {tan}^{2} (x)} = 3$ $2/(1-tan^2(x)) = 3$

Which is obviously false, as the tangent range from $- \infty$ $-oo$ to $\infty$ $oo$ .
If you continue to work this like it was an equation, you'll see this only has two tangent values for solutions, $\pm \frac{\sqrt{3}}{3}$ $+-sqrt(3)/3$ .

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How do you prove the identity $tan 2 X cot X = 3$ $tan2XcotX=3$ ?

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Explanation:

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How do you prove the identity tan2XcotX=3tan2XcotX=3tan2XcotX=3?

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Explanation:

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How do you prove the identity $tan 2 X cot X = 3$ $tan2XcotX=3$ ?