Question 382048
I hope you meant {{{sin^4 (x)}}} instead of {{{sin (4x)}}}. I first thought it was the latter interpretation which is not true for all x, but then noticed that the first interpretation yielded a true identity, which I'll explain below:

First note that tan x cot x = 1 (given that tan x and cot x are nonzero). The expression

{{{sin^4 (x) + 2 sin^2 (x) cos^2 (x) + cos^4 (x)}}} factors to

{{{(sin^2 (x) + cos^2 (x))^2}}}

Since {{{sin^2 (x) + cos^2 (x) = 1}}}, and {{{1^2 = 1}}}, both sides are equal to 1, and we are done.

Next time, I would encourage you to put the caret ("^") sign to denote an exponent, to make the question less ambiguous.