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

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Answer 1 · 2016-06-02T03:45:01

Start by putting on a common denominator.

#(sin theta xx sin theta)/((1 + costheta) xx sin theta) + ((1 + costheta) xx(1+ costheta))/(sin theta xx (1 + costheta))#

=#(sin^2theta + 1 + 2costheta + cos^2theta)/(sin theta xx (1 + costheta)#

Using the pythagorean identity #cos^2theta + sin^2theta = 1#

#=(2 + 2costheta)/(sin theta xx(1+ costheta)#

#= (2(1 + costheta))/(sin theta xx (1 + costheta)#

#= 2/sintheta#

Now recall that #1/sintheta = csctheta#

#=2csctheta#

Hopefully this helps!