Simplify: (cos y) / ( sec y - tan y)​

"Answer:

1 + sin(y).

Step-by-step explanation:

First, we rewrite sec(y) and tan(y) in terms of sin(y) and cos(y) by using the reciprocal identity for secant and the quotient identity for tangent:

Next, simplify the denominator:

Then, simplify the complex fraction:

For cos²(y), use the Pythagorean identity and rewrite using cos²(y) = 1 - sin²(y):

Notice that the numerator, 1 - sin²(y) is a difference of two squares. So, we rewrite it as (1 + sin(y))(1 - sin(y)):

Then cancel 1 - sin(y) from both the numerator and denominator. So, we are left with

So, the answer is 1 + sin(y)."