Answer:
A) -2cot(x)csc(x)
Step-by-step explanation:
[tex]\frac{1}{cos(x)+1} +\frac{1}{cos(x)-1}[/tex]
[tex]=\frac{cos(x)-1}{(cos(x)+1)(cos(x)-1)} +\frac{cos(x)+1}{(cos(x)+1)(cos(x)-1)}[/tex]
[tex]=\frac{2cos(x)}{(cos(x)+1)(cos(x)-1)}[/tex]
[tex]=\frac{2cos(x)}{cos^2(x)-1}[/tex]
[tex]=\frac{2cos(x)}{(1-sin^2(x))-1}[/tex]
[tex]=\frac{2cos(x)}{-sin^2(x)}[/tex]
[tex]=-2\frac{cos(x)}{sin(x)}\cdot\frac{1}{sin(x)}[/tex]
[tex]=-2cot(x)csc(x)[/tex]
