Verifying a trigonometric identity for the values of cos^2(t

[chromechris]

The Pythagorean identities state that: cos^2(theta) = 1-sin^2(theta) . The power-reducing formulas state that cos^2(theta) = (1+cos(theta))/2. I set up an equation with both of these values at either end of the equation, and tried to verify their quality using trigonometric identities rules, but I am unable to determine that these two are equal? Are these two values equal?

[Guest]

[tex]cos^{2}[/tex][tex]\frac{\alpha}{2}[/tex]= [tex]\frac{1+cos\alpha}{2}[/tex]

[tex]\frac{1+cos\alpha}{2}[/tex]=[tex]\frac{1+cos[ 2(\frac{\alpha}{2}) ]}{2}[/tex]=

=[tex]\frac{1+2cos^{2} \frac{\alpha}{2}-1}{2}[/tex]=

=[tex]cos^{2}[/tex][tex]\frac{\alpha}{2}[/tex]