How do you prove $1+tan^2 (x) = sec^2 (x)$ ?

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Answer 1 · 2016-10-01T00:22:08

See explanation...

Starting from:

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

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

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

which simplifies to:

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

How do you prove 1+tan^2 (x) = sec^2 (x)1+tan^2 (x) = sec^2 (x)?