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)#