You need to recognize the formula tan(a+b) = (tan a + tan b)/(1- tan a*tan b). You need to put a = 2x and b = x , such that:
tan(2x + x) = (tan 2x + tan 6x)/(1 - tan 2x*tan x)
tan 3x= (tan 2x + tan 6x)/(1 - tan 2x*tan x)
Hence, the given expression could be evaluated as the tangent of the sum of angles 2x and x , such that (tan 2x + tan 6x)/(1 - tan 2x*tan x) = tan 3x.
Monday, August 5, 2019
Precalculus, Chapter 5, 5.4, Section 5.4, Problem 34
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