How do you simplify the expression $(1-tan^2t)/(1+tan^2t)+1$ ?

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Answer 1 · 2016-10-11T13:24:10

$=(1 - sin^t/cos^2t)/(1 + sin^2t/cos^2t) + 1$

$=((cos^2t - sin^2t)/cos^2t)/((cos^2t + sin^2t)/(cos^2t)) + 1$

$=(cos^2t - sin^2t)/(cos^2t) xx cos^2t/(cos^2t + sin^2t)$

Apply the identity $sin^2theta + cos^2theta = 1$ .

$=cos^2t - sin^2t$

$=1 - sin^2t - sin^2t$

$= 1 - 2sin^2t$

Apply the double angle identity $cos2theta = 1 - 2sin^2theta$ .

$=cos2t$

Hopefully this helps!

How do you simplify the expression (1-tan^2t)/(1+tan^2t)+1(1-tan^2t)/(1+tan^2t)+1?