Question

Simplify the expression

Answer 1

`(2)/(cos(x))`

Explanation:

Key facts you will need to know to solve this

`tan(x) = (sin(x))/(cos(x))`

`sin^2 + cos^2 = 1` so
`1-sin^2= cos^2`

The equation can also simplify by cross multiplying the fraction to make:

`(cosx-sincosx)/((1+sinx)(1-sinx)) + (cosx+sincosx)/((1-sinx)(1+sinx))`

`(cosx-sincosx)/(1-sin^2(x)) + (cosx+sincosx)/(1-sin^2(x))` =
`(2cos(x))/(1-sin^2(x))`

Using the equation
`1-sin^2= cos^2` that we established earlier, the fraction is also:

`(2cos(x))/(cos^2(x))` =
`(2)/(cos(x))`

Therefore, the answer is
`(2)/(cos(x))`