How do you simplify \(\frac{\sin x}{1+\sin x}-\frac{\sin x}{1-\sin x} ?\)
Answer:
You should get \(-2 \tan ^{2} x\) as a final answer.
Explanation:
Using the pythagorean identity \(\cos ^{2} x+\sin ^{2} x=1\)
\(=\frac{-2 \sin ^{2} x}{\cos ^{2} x}\).
Using the quotient identity \(tan x=\frac{\sin x}{\cos x}\).
\(=-2 \tan ^{2} x\)
Hopefully this helps!