Solving Trig Theta Question: 1/sin(theta)-cos(theta)/sin(theta)

[Mejiera]

Homework Statement

I don't understand the step the math book took to convert sin(theta)/sin(theta)-cos(theta) to 1/sin(theta)-cos(theta)/sin(theta)

Homework Equations

The Attempt at a Solution

 

[Rasalhague]

It just divided the whole expression by sin(theta).

sin(theta)/sin(theta) - cos(theta) = 1 - cos(theta). Divide that by sin(theta) and you get 1/sin(theta) - cos(theta)/sin(theta).

But in general 1 - cos(theta) does not equal 1/sin(theta) - cos(theta)/sin(theta).