How do you simplify Cos theta/(1 + sin theta) + tan theta?

1 Answer
Mar 13, 2018

sec theta

Explanation:

=cos theta/(1+sin theta)+tan theta
=cos theta/(1+sin theta)+sin theta/cos theta
->Get a common denominator
=cos theta/(1+sin theta) * cos theta/cos theta +sin theta/cos theta* (1+sintheta)/ (1+sintheta)
=(cos^2 theta+sin theta+ sin^2theta)/(costheta(1+sin theta)
->cos^2theta+sin^2theta = 1
=(sin theta + 1)/(cos theta (1+sin theta))
-> Cancel out in numerator and denominator
=1/costheta
=sectheta