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

Question

40935 views around the world

You can reuse this answer
Creative Commons License

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!

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