# Thread: Trig Identity - Im so confused!

1. ## Trig Identity - Im so confused!

This is my first post. Up until this point I have been able to figure out things by myself but these trig identities are killing me. The ones in my textbook I can figure out but the identities my teacher gives are not as clear to me. Here is the one I am I currently stuck on.

1-1/2sin(2x)=sin^3(x)+cos^3(x)/sin(x)+cos(x)

I'm not sure where to start. Perhaps the right side?

I hope I formatted it right. I don't know how to make it look pretty.

Thanks for any help!

2. Originally Posted by repete
This is my first post. Up until this point I have been able to figure out things by myself but these trig identities are killing me. The ones in my textbook I can figure out but the identities my teacher gives are not as clear to me. Here is the one I am I currently stuck on.

1-1/2sin(2x)=sin^3(x)+cos^3(x)/sin(x)+cos(x)

I'm not sure where to start. Perhaps the right side?

I hope I formatted it right. I don't know how to make it look pretty.

Thanks for any help!
Is this the identity you're trying to prove:

$1-\frac{1}{2sin(2x)}=\frac{sin^3(x)+cos^3(x)}{sin(x) +cos(x)}$

??

3. How do you make it look like that? I'm guessing its code?

That's very close except the left side is...

1-(1/2sin(2x))

Hopefully the parentheses makes it clear.

4. The first thing you can do to the right side is cancel out the denominator by factoring the numerator as the sum of two cubes.

5. Originally Posted by repete
How do you make it look like that? I'm guessing its code?

That's very close except the left side is...

1-(1/2sin(2x))

Hopefully the parentheses makes it clear.

http://www.mathhelpforum.com/math-he...-tutorial.html

There is a PDF file that you can view.

6. The right side can be simplified down to this:

$\frac{sin^3(x)+cos^3(x)}{sin(x)+cos(x)}=\frac{[sin(x)+cos(x)][cos^2(x)-sin(x)cos(x)+sin^2(x)]}{sin(x)+cos(x)}$

$=cos^2(x)-sin(x)cos(x)+sin^2(x)$

$=1-sin(x)cos(x)$

I guess your left side must be:

$1-\frac{1}{2}sin(2x)$

$=1-\frac{1}{2}(2sin(x)cos(x))$

$=1-sin(x)cos(x)$

7. Thanks adkinsjr! I didn't even think about factoring it. I was able to prove it myself with that step in. I'm sure I will be back with more identities. Thanks again!