How do you write tan(2x) in terms of cot(x)? Thank you!

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Answer 1 · 2017-09-24T13:57:58

Start with the identity for $tan(2x)$
Multiply the right side by 1 in the form of $cot^2(x)/cot^2(x)$
Perform the multiplication and simplify.

The identity for $tan(2x)$ is:

$tan(2x) = (2tan(x))/(1 - tan^2(x))$

Multiply the right side by 1 in the form of $cot^2(x)/cot^2(x)$ :

$tan(2x) = cot^2(x)/cot^2(x)(2tan(x))/(1 - tan^2(x))$

Multiply the numerators and the denominators respectively:

$tan(2x) = (2tan(x)cot^2(x))/(cot^2(x) - cot^2(x)tan^2(x))$

Use the identity $cot(x)tan(x) = 1$ , to simplify:

$tan(2x) = (2cot(x))/(cot^2(x) - 1)$