Question

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

Answer 1

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

Explanation:

`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`