How do you identify $tantheta/(1-cos^2theta)$ ?

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Answer 1 · 2017-01-30T00:38:32

The expression can be simplified to $secthetacsctheta$

First of all, apply the identity $sin^2theta + cos^2theta = 1 -> sin^2theta = 1 - cos^2theta$ :

$=tantheta/sin^2theta$

Now convert $tantheta$ to $sintheta/costheta$ .

$=(sin theta/costheta)/sin^2theta$

$= sin theta/costheta * 1/sin^2theta$

$=1/(costhetasintheta)$

Apply the identities $1/costheta = sectheta$ and $1/sintheta = csctheta$ .

$=secthetacsctheta$

Hopefully this helps!

How do you identify tantheta/(1-cos^2theta)tantheta/(1-cos^2theta)?