How do you prove the identity $cos^2theta(1 + tan^2theta) = 1$ ?

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Answer 1 · 2015-08-15T04:30:23

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

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

How do you prove the identity cos^2theta(1 + tan^2theta) = 1cos^2theta(1 + tan^2theta) = 1?