Question

Simplify the trigonometric expression.

Answer 1

first some algebra
\[\frac{1}{1+x}+\frac{1}{1-x}=\frac{2}{1-x^2}\]

Answer 2

In a few words: Take LCM

Answer 3

then replace \(x=\sin(\theta)\) to get
\[\frac{2}{1-\sin^2(\theta)}\]

Answer 4

mhmm..

Answer 5

then note that since
\(sin^2(\theta)+\cos^2(\theta)=1\) we know \(1-\sin^2(\theta)=\cos^2(\theta)\) giving you
\[\frac{2}{\cos^2(\theta)}\]

Answer 6

finally since \(\frac{1}{\cos(\theta)}=\sec(\theta)\) you can write this as
\[2\sec^2(\theta)\]

Answer 7

Okay. I found it. Thank you.