Prove that $(1+tan^2x)cos^2x=1$ ?

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Answer 1 · 2018-04-19T18:57:35

See below

We will use the following identities

$cos^2x+sin^2x=1$

$sec^nx=1/cos^nx$

$tan^nx=sin^nx/cos^nx$

Proof

We start by manipulating the first identity

$cos^2x+sin^2x=1$

$rArr cos^2/cos^2x+sin^2x/cos^2x=1/cos^2x$

$rArr1+tan^2x=sec^2x$

So

$(1+tan^2x)cos^2x=sec^2xcos^2x=1/cos^2xcos^2x=1$ $color(white)(aaaa)square$

Prove that (1+tan^2x)cos^2x=1(1+tan^2x)cos^2x=1?