Half Angle Formula: Solving the Homework Statement

[tweety1234]

Homework Statement

Can someone please explain how my book got $sin^{2} \theta = \frac{1-cos2\theta}{2}$ and $cos^{2}\theta = \frac{1+cos2\theta}{2}$

As I thought the half angle formula's were $sin \frac{\theta}{2} = \sqrt{\frac{1-cos\theta}{2}}$

$cos\frac{\theta}{2} = \sqrt\frac{1+cos\theta}{2}}$

So how can it also be the top one's aswell?

Thanks.

 

[Doc Al]

Replace θ with 2θ.

 

[tweety1234]

Replace θ with 2θ.

Oh I see, can't believe I missed that.

Thanks.