Question #58cc8

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Answer 1 · 2016-07-27T16:57:41

see explanation

Rewrite as:

$cos^2(x)(1 +cos^2(x)) = 1$

Divide both sides by $cos^2(x)$ :

$1+cos^2(x) = sec^2(x)$

Take $sin^2x + cos^2x =1$ and divide by $cos^2x$ to get:

$tan^2x + 1 = sec^2x$

$implies 1 + cos^2(x) = 1 + tan^2(x)$

$implies cos^2(x) = tan^2(x)$

Divide by $cos^2(x)$ both sides:
$1 = tan^2(x)*1/cos^2(x)$
or
$1 = tan^2(x)*sec^2(x)$

$therefore$ statement becomes

$tan^2(x)(1+tan^2(x)) = 1$

$implies tan^2(x) + tan^4(x) = 1$ as required