I'm reading this explanation of integrals with quadratics and the author pulled this out of nowhere. Is it obvious to everyone but me that this statement is true?
Is there an easy way to see that $\left(2 \tan^2x+2\right)^3 = 8\left(\tan^2x+1\right)^3$?
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calculus
algebra-precalculus
integration
trigonometry
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0$(2a^2+2)^3=[2(a^2+1)]^3=2^3(a^2+1)^3$ This is true for any $a$, for $a=\tan x$ you get your equality. – 2013-08-05
1 Answers
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Since $2\tan^2 x + 2 = 2(\tan^2 x + 1),$ we see that $(2\tan^2 x + 2)^3 = 2^3(\tan^2 x + 1)^3.$
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0*facepalm. It's so obvious. Than$k$s. – 2012-10-19