Verify the following identities (a) tan 3x =[ tan x(3-tan²x]/(1-3tan²x)?

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1 Answer
Sonnhard
May 27, 2018

The proof for a)

Explanation:

We have
#tan(x+2x)=(tan(x)+tan(2x))/(1-tan(x)tan(2x))#
#tan(2x)=2tan(x)/(1-tan(x)^2)#
Putting things together:

#tan(3x)=(tan(x)+2tan(x)/(1-tan^2(x)))/(1-tan^2(x))/(1-tan(x)*(2tan(x)/(1-tan^2(x)))#
Multiplying denominator and numerator by
#1-tan^2(x)#
#tan(3x)=(tan(x)-tan^3(x)+2tan(x))/(1-tan^2(x)-2tan^2(x))#
and this is
#tan(3x)=(tan(x)*(3-tan^2(x)))/(1-3tan^2(x))#

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