Use the fundamental identities and appropriate algebraic operations to simplify the expression.

cosx / (1+sinx)

Answer: secx

Can someone please assist as to how I get to the answer?

You must have a typo

cosx/(1+sinx) is NOT equal to secx

try it with any angle.

To simplify the expression cosx / (1+sinx), we can start by using the fundamental identity:

secx = 1 / cosx

From this identity, we can rewrite the denominator (1+sinx) as:

1 + sinx = cos^2x / cosx + sinx = (cos^2x + sinx * cosx) / cosx

Now, we can rewrite the initial expression as:

cosx / (1+sinx) = cosx / (cos^2x + sinx * cosx) / cosx

Simplifying further, we can cancel out the common factors of cosx:

cosx / (cos^2x + sinx * cosx) / cosx = 1 / (cos^2x + sinx * cosx)

Now, let's express sinx * cosx as sinx * cosx = sinx * cosx / cos^2x * cos^2x = tanx / cosx

Substituting this back into the expression:

1 / (cos^2x + sinx * cosx) = 1 / (cos^2x + tanx / cosx)

Using the fundamental identity:

tan^2x + 1 = sec^2x

We can rewrite the expression as:

1 / (cos^2x + tanx / cosx) = 1 / (cos^2x + tan^2x / cos^2x) = 1 / (cos^2x + sec^2x) = 1 / sec^2x = sec^2x

Therefore, the simplified expression is sec^2x (secant squared x).