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

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Answer 1 · 2017-03-09T16:51:52

Please see below.

$cos^2+tan^2cos^2x$

= $cos^2+sin^2x/cos^2x xxcos^2x$

= $cos^2+sin^2x/cancel(cos^2x) xxcancel(cos^2x)$

= $cos^2+sin^2x$

= $1$

Answer 2 · 2017-03-09T16:53:02

Factor out $cos^2x$ .

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

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

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

Use the identity $secx= 1/cosx$ .

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

$1 = 1$

This identity is true.

Hopefully this helps!

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