Question 235426
{{{tan^2(x)+cot^2(x)=(1-2sin^2(x)+2sin^4(x))/(sin^2(x)-sin^4(x))}}}
{{{tan^2(x)+cot^2(x)=(1-2sin^2(x)+2sin^4(x))/(sin^2(x))*(1-sin^2(x))}}}
{{{tan^2(x)+cot^2(x)=(1-2sin^2(x)+2sin^4(x))/(sin^2(x))*(cos^2(x))}}}
{{{sin^2(x)/cos^2(x) + cos^2(x)/sin^2(x) = (1-2sin^2(x)+2sin^4(x))/(sin^2(x))*(cos^2(x))}}}
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{{{(sin^4(x) + cos^4(x))/(sin^2(x)*cos^2(x)) = (1-2sin^2(x)+2sin^4(x))/(sin^2(x)*(cos^2(x)))}}}
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{{{sin^4(x) + cos^4(x) = 1-2sin^2(x)+2sin^4(x)}}}
{{{cos^4(x) = 1 - 2sin^2(x) + sin^4(x)}}}
{{{(1-sin^2(x))^2 = 1 - 2sin^2(x) + sin^4(x)}}}
{{{1 - 2sin^2(x) + sin^4(x) = 1 - 2sin^2(x) + sin^4(x)}}}
QED