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

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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