# Thread: Help with Trigonometric Identities

1. ## Help with Trigonometric Identities

Sorry for another one but this one is giving me a lot of trouble.

$\displaystyle sin^3{x}cos^2{x}=cos^2{x}sin{x}-cos^4{x}sin{x}$

I assume you would start with the right side since it's the harder side.
I tried changing $\displaystyle cos^2{x}\Rightarrow1-sin^2{x}$ from the RHS, but end up no where. I'm confused at what I should just keep and what I should change with the identity:

$\displaystyle cos^2{x}+sin^2{x}=1$

Edit: Didn't realize there was a sub forum specifically for Trigonometry. Can I move this thread?

2. Originally Posted by toeknee
Sorry for another one but this one is giving me a lot of trouble.

$\displaystyle sin^3{x}cos^2{x}=cos^2{x}sin{x}-cos^4{x}sin{x}$

I assume you would start with the right side since it's the harder side.
I tried changing $\displaystyle cos^2{x}\Rightarrow1-sin^2{x}$ from the RHS, but end up no where. I'm confused at what I should just keep and what I should change with the identity:

$\displaystyle cos^2{x}+sin^2{x}=1$

Edit: Didn't realize there was a sub forum specifically for Trigonometry. Can I move this thread?

$\displaystyle cos^2{x}sin{x}-cos^4{x}sin{x}=cos^2{x}sin{x}(1-cos^2{x})=cos^2{x}sin{x}sin^2{x}=cos^2{x}sin^3{x}$

3. How does $\displaystyle cos^4{x}sin{x}$ change to $\displaystyle 1-cos^2{x}$?

4. It doesn't "change". He factored out $\displaystyle \cos^2 x \sin x$ since it's common to both terms.

In general, $\displaystyle ab+ac=a(b+c)$

5. Originally Posted by toeknee
How does $\displaystyle cos^4{x}sin{x}$ change to $\displaystyle 1-cos^2{x}$?
It's not. I just pulled out cos^2{x}sin{x} from cos^2{x}sin{x} and cos^4{x}sin{x}=cos^2{x}cos^2{x}sin{x}