How do you use the fundamental identities to simplify $cost(1+tan^2t)$ ?

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Answer 1 · 2017-01-26T09:28:11

$cos t(1+tan^2 t) = 1/cos t=sec t$

$cos t(1+tan^2 t) = cos t(sec^2 t)$

where $tan^2 t + 1 =sec^2 t=1/cos^2 t$

$cos t(1+tan^2 t) = cos t(1/cos^2 t)$

$cos t(1+tan^2 t) = cancelcos t(1/cos^cancel2 t)$

$cos t(1+tan^2 t) = 1/cos t=sec t$

How do you use the fundamental identities to simplify cost(1+tan^2t)cost(1+tan^2t)?