Question

Simplify; cot^2 x - csc^2 x

Answer 1

This is actually a demoninator, but I already simplified the numerator which was originaly "cos^2 x + sin^2 x" into 1.

Answer 2

it is pythagorean, much like the first identity you described... it would be -1

Answer 3

Oh, I see. I don't really need an explanation but I'm interested into how you got that.

Answer 4

http://www.regentsprep.org/Regents/math/algtrig/ATT9/pythag12.gif

Answer 5

see the last formulat on that picture? solve by \(\large cot^2(\theta)\)

Answer 6

I remember my pythagorean's by taking the original cos^2(x)+sin^2(x)=1 and dividing each term by either of the terms... such as, divide each term by cos^2(x)... leads to 1+tan^2(x)=sec^2(x).... the other one you get by dividing each term by sin^2(x).

Answer 7

@jdoe I don't know what to do with the cot ._.

Answer 8

That's right @jdoe0001, just like that.

Answer 9

I guess this just goes to show I've got plenty of tutoring sessions to attend. Thanks you two!

Answer 10

You're welcome.

Answer 11

$$
1+cot^2(\theta)=\color{blue}{csc^2(\theta)} \implies cot^2(\theta)=\color{blue}{csc^2(\theta)}-1
$$