How do you simplify $(1 + tan^2 x)(cos^2 x)$ ?

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Answer 1 · 2015-08-12T15:45:21

Simplify: (1 + tan^2 x) (cos^2 x)

Ans: 1

$(1 + sin^2 x/cos^2x) cos^2 x = [(cos^2 x + sin^2 x)/cos^2 x]cos^2 x =$

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

Answer 2 · 2015-08-12T17:00:31

You can use two identities:

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

Therefore:

$= sec^2x*cos^2x = cos^2x/cos^2x = 1$

How do you simplify (1 + tan^2 x)(cos^2 x)(1 + tan^2 x)(cos^2 x)?