Question

Question #19476

Answer 1

See answer below.

Explanation:

`secy+tany=1/cosy+siny/cosy=(cosy+cosysiny)/cos^2y=`

`=(cosy(1+siny))/(1-sin^2y)=(cosy(cancel(1+siny)))/((cancel(1+siny))(1-siny))=cosy/(1-siny)`

Let's break this down:

1. Rewrite `secy` and `tany` as `1/cosy` and `siny/cosy`
2. Add the two fractions
3. Take a factor of `cosy` from the numerator
4. Rewrite `cos^2y` as `1-sin^2y` using `cos^2y+sin^2y=1`
5. Rewrite `1-sin^2y` using the difference of two squares identity
6. Cancel the common factors