a) You need to bring the terms to a common denominator such that:

`(cos x*(1+sin x) - cos x*(1 - sin x))/((1+sin x)(1 - sin x)) = 2 tan x`

You need to open the brackets such that:

`(cos x + cos x*sin x - cos x + cos x* sin x)/(1 - sin^2 x) = 2 tan x`

Reducing like terms yields:

`(2cos x*sin x)/(1 - sin^2 x) = 2 tan x`

You need to remember that `1 - sin^2 x = cos^2 x` such that:

`(2cos x*sin x)/(cos^2 x) = 2 tan x`

Reducing by `cos x ` yields:

`(2sin x)/(cos x) = 2 tan x`

You need to substitute `sin x/cos x` by tan x such that:

`2 tan x = 2 tan x`

**Hence, using formulas of trigonometry and the laws applied to
difference of fractions that have different denominators yields that
`cosx/(1-sinx) - cosx/(1+sinx) =2 tanx` .**

b) You need to multiply by `cos x(1 + cos x)` both sides such that:

`(1 - sin x)(1 + cos x) = sin x*cos x`

You need to open the brackets such that:

`1 + cos x - sin x - sin x*cos x = sin x*cos x`

`1 + cos x - sin x = 2 sin x*cos x`

`1 + cos x - sin x = sin 2x`

**Hence, making transformations to the left side yields that the
expression `(1-sinx)/cosx != sinx/(1+cosx).`**

## See eNotes Ad-Free

Start your **48-hour free trial** to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Already a member? Log in here.