1. Integration by evaluation

I need some help with an integration question that's been bugging me. I just can't identify the conclusions applied to the following jump:

integral of 1 - 0.5sin squared 2theta dtheta (between 0 and pi/2) = integral of 1 - 0.25(1 - cos4theta) dtheta (between 0 and pi/2)

can anyone help?

Thank you

2. Originally Posted by maggiec
I need some help with an integration question that's been bugging me. I just can't identify the conclusions applied to the following jump:

integral of 1 - 0.5sin squared 2theta dtheta (between 0 and pi/2) = integral of 1 - 0.25(1 - cos4theta) dtheta (between 0 and pi/2)

can anyone help?

Thank you
used the power reduction identity ...

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

3. Originally Posted by skeeter
used the power reduction identity ...

$\sin^2{u} = \frac{1 - \cos(2u)}{2}$
Can I also ask, what is this identity a derivation of?
Thanks

4. Originally Posted by maggiec
Can I also ask, what is this identity a derivation of?
Thanks
Double-Angle and Half-Angle Formulas