# Help with Trigonometric Identities

• Feb 16th 2011, 04:02 PM
toeknee
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?
• Feb 16th 2011, 04:25 PM
Also sprach Zarathustra
Quote:

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?

$\displaystyle cos^2{x}sin{x}-cos^4{x}sin{x}=cos^2{x}sin{x}(1-cos^2{x})=cos^2{x}sin{x}sin^2{x}=cos^2{x}sin^3{x}$
• Feb 16th 2011, 04:43 PM
toeknee
How does $\displaystyle cos^4{x}sin{x}$ change to $\displaystyle 1-cos^2{x}$?
• Feb 16th 2011, 04:46 PM
DrSteve
It doesn't "change". He factored out $\displaystyle \cos^2 x \sin x$ since it's common to both terms.

In general, $\displaystyle ab+ac=a(b+c)$
• Feb 16th 2011, 04:47 PM
Also sprach Zarathustra
Quote:

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}