Question

prove the identity
1/(csc theta + cot theta) = csc theta - cot theta

Answer 1

Use identities: csc(theta) = 1/cos(theta), cot(theta) = cos(theta)/sin(theta). If you have 1/cos(theta), then the cosine and sine reciprocate.

You can combine fractions by finding the least common denominators. There's also the very important identity where:
sin(theta)^2 + cos(theta)^2 = 1

Because this, you can subtract cosine^2 from both sides to get
sin(theta)^2 = 1 - cos(theta)^2

Or the sine from both sides to get another identity. You can also divide both sides by cosine^2, to get:
tan(theta)^2 + 1 = 1/cos(theta)^2 = sec(theta)^2

If you do the same with sine^2 you will get an identity involving csc and cot.

Many identities. You must know them, or know how to derive them.

Answer 2

I know identities.. struggling with algebra

Answer 3

This is trigonometry...not algebra...