2 Problems/Trig Function and Identity

[APHELION]

Hello everyone. I officially have the worst Trig teacher in America and I have never been so confused in a math class before. I have at least 5 problems (only 2 posted here) I'm struggling with and need to figure out before my exam tomorrow. Any help is much appreciated.

1.

Homework Statement

The function f(x) = x - sin x is odd. True or False?

Homework Equations

The Attempt at a Solution

From my professors review I know it's True but his explanation was so unclear I don't know why. ??2.

Homework Statement

sin$$\alpha$$$$/$$1-cos$$\alpha$$- sin$$\alpha$$$$/$$1+cos$$\alpha$$=

Homework Equations

The Attempt at a Solution

I ended up with 0 as the solution. ??

 

[Bohrok]

For a function to be odd, it must satisfy f(-x) = -f(x)
Try applying that to your function.

Is this what you mean for the second one?
$$\frac{sin\alpha}{1 - cos\alpha} - \frac{sin\alpha}{1 + cos\alpha}$$

Are you supposed to simplify it or prove an identity?

 

[APHELION]

So on the function problem I need to substitute -x and -f into the equation and solve?

On the identity problem they want to me simplify and yes you have it correct above.

 

[Bohrok]

With your f(x), evaluate f(-x) and see if you get -f(x). If you do, then f(x) is an odd function.

For the other problem, show what you tried; I don't think it's equal to 0.

 

[APHELION]

Cool, I was able to get -f(x) on the first one.

Honestly I feel really stupid on the second one. I don't know where to start other than getting a common denominator and then evaluating? Is that even how it would go?

That's probably way wrong but that's why I'm here lol...

 

[Bohrok]

Try multiplying by the conjugates of the denominators to simplify. That's one of the first things you should try doing with trig problems like this.

 

[emyt]

trig functions are just functions of numbers like anything else, you shouldn't think that you aren't allowed to take common denominators..et c and everything else.

for your question, the denominators 1- cos x and 1+cosx, the answer should be fairly clean. And when you get stuck simplifying, keep other known identities in mind (like the Pythagorean theorem).

The answer isn't 0