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

1 Answer
Richard
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#

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