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

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Answer 1 · 2015-08-27T19:08:31

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

$(1+tan^2(theta))(cos^2(theta))$

$=(cos^2(theta)/cos^2(theta)+sin^2(theta)/cos^2(theta))(cos^2(theta))$

$=((cos^2(theta)+sin^2(theta))/cos^2(theta))cos^2(theta)$

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

...using $cos^2(theta) + sin^2(theta) = 1$

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