SOLUTION: Factor and simplify using fundamental identities: tan^4x+2tan^2x+1

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Question 105525: Factor and simplify using fundamental identities:
tan^4x+2tan^2x+1
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
Let y=%28tan+x%29%5E2

Then,
y%5E2%2B2y%2B1=0

Please read my lesson,"Factoring trinomials: SHORTCUT!!!"

By the quadratic formula,
y=%28-2%2B-sqrt%282%5E2-4%2A1%2A1%29%29%2F%282%2A1%29
y=%28-2%2B-sqrt%284-4%29%29%2F%282%29
y=%28-2%2B-sqrt%280%29%29%2F%282%29
y=%28-2%2B-+0%29%2F%282%29
y=-2%2F2
y=-1
Thus,
%28tan+x%29%5E2=-1
%28tan+x%29%5E2%2B1=0
So, this means that the equation is a perfect square trinomial and that:

%28tan+x%29%5E4%2B2%28tan+x%29%5E2%2B1=%28%28tan+x%29%5E2%2B1%29%5E2

Power up,
HyperBrain!