Question

How do you simplify `cos^2B / (1-sinB)`?

Answer 1

`(cos^2(B))/(1-sin(B)) = 1+sin(B)`

Explanation:

Based on the definitions of `sin` and `cos` and on the Pythagorean Theorem
`color(white)("XXX")cos^2(B)+sin^2(B) = 1`
or
`color(white)("XXX")cos^2(B) = 1-sin^2(B)`

`color(white)("XXXXXXX")=(1-sin(B))*(1+sin(B))`

Therefore
`color(white)("XXX")(cos^2(B))/(1-sin(B)) = (cancel((1-sin(B)))*(1+sin(B)))/(cancel((1-sin(B)))`