How do you show that $sintheta(cot theta + tantheta) = sec theta$ ?

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Answer 1 · 2017-03-13T16:01:19

Apply the identities $cottheta = costheta/sintheta$ and $tantheta = sintheta/costheta$ .

$sintheta(costheta/sintheta + sintheta/costheta) = sectheta$

$costheta + sin^2theta/costheta = sectheta$

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

Apply $cos^2theta + sin^2theta = 1$ :

$1/costheta = sectheta$

This is true, by the identity $sectheta = 1/costheta$ .

Hopefully this helps!

How do you show that sintheta(cot theta + tantheta) = sec thetasintheta(cot theta + tantheta) = sec theta?