Sin(theta)/1+cos(theta)=1-cos(theta)/sin(theta) can someone help?

1 Answer
May 10, 2018

theta ne npi, n in ZZ

Explanation:

First, please use math template, it is very frustrating to read something like this, and ask a precise question, I assume you want to find theta but I am not a mind reader.

frac{sin(theta)}{1+cos(theta)}=frac{1-cos(theta)}{sin(theta)}

We can suppose 1+cos(theta) and sin(theta) to be nonzero, otherwise the expression does not make sense, so we can multiply by 1+cos(theta)sin(theta) and get

sin^2(theta)=(1-cos(theta))(1+cos(theta))=1-cos^2(theta)=sin^2(theta)

So we get the tautology sin^2(theta)=sin^2(theta), true for all theta that make sense, so we just need to exclude the ones such that sin(theta)=0 and cos(theta)=-1. So theta ne npi and theta ne (2n+1)pi, in particular since the second is weaker then the first we conclude.