1. ## Prove the Identity

sin^4u-cos^4u=-cos(2u)

Would you use the power reduction formulas or what?

2. $\displaystyle \sin^4{u} - \cos^4{u} \equiv (\sin^2{u} - \cos^2{u})(\sin^2{u} + \cos^2{u})$

$\displaystyle \equiv -(\cos^2{u} - \sin^2{u})(1)$

$\displaystyle \equiv -\cos{2u}$.

3. how did you get from -(cos^2u-sin^2u)(1) to -cos2u?

4. You should be aware of the well-known identity $\displaystyle \cos{2x} \equiv \cos^2{x} - \sin^2{x}$.

5. yes yes yes, thank you!