I have two questions below.

Establish each identity.

(1) cos(x)/[1 - tan(x)] + sin(x)/[1 - cot(x)] = sin(x) + cos(x)

This is my set up for question 1:

Let tan(x) = sin(x)/cos(x)

Let cot(x) = cos(x)/sin(x)

After plugging and simplifying the complex fractions, I get this on the left side:

cos^2 (x)/[cos(x) - sin(x)] + sin^2 (x)/[sin(x) - cos(x)]

Where do I go from there?

Question 2:

3 sin^2 (x) + 4 cos^2 (x) = 3 + cos^2 (x)

I know that sin^2 (x) = 1 - cos^2 (x)

This is my set up:

3[1 - cos^2 (x)] + 4 cos^2 (x) = 3 + cos^2 (x)

I then use the distributive rule on the left side and get this:

3 - 3cos^2 (x) + 4 cos^2 (x) = 3 + cos^2 (x)

Where do I go from there?

Thanks