Answer:
[tex]\frac{2}{cos(x)}[/tex]
Step-by-step explanation:
Key facts you will need to know to solve this
[tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex]
[tex]sin^2 + cos^2 = 1[/tex] so [tex]1-sin^2= cos^2[/tex]
The equation can also simplify by cross multiplying the fraction to make:
[tex]\frac{cosx-sincosx}{(1+sinx)(1-sinx)} + \frac{cosx+sincosx}{(1-sinx)(1+sinx)}[/tex]
[tex]\frac{cosx-sincosx}{1-sin^2(x)} + \frac{cosx+sincosx}{1-sin^2(x)}[/tex] = [tex]\frac{2cos(x)}{1-sin^2(x)}[/tex]
Using the equation [tex]1-sin^2= cos^2[/tex] that we established earlier, the fraction is also:
[tex]\frac{2cos(x)}{cos^2(x)}[/tex] = [tex]\frac{2}{cos(x)}[/tex]
Therefore, the answer is [tex]\frac{2}{cos(x)}[/tex]
