Step-by-step explanation:
[tex] \sin^2 (\frac{\pi}{4} - \alpha) = \frac{1}{2}(1 - \sin 2\alpha) [/tex]
Use the identity
[tex] \sin^2 \theta = \dfrac{1 - \cos 2\theta}{2} [/tex]
on the left side.
[tex] \dfrac{1 - \cos [2(\frac{\pi}{4} - \alpha)]}{2} = \frac{1}{2}(1 - \sin 2\alpha) [/tex]
[tex] \dfrac{1 - \cos (\frac{\pi}{2} - 2\alpha)}{2} = \frac{1}{2}(1 - \sin 2\alpha) [/tex]
Now use the identity
[tex] \sin \theta = \cos(\frac{\pi}{2} - \theta) [/tex]
on the left side.
[tex] \dfrac{1 - \sin 2\alpha}{2} = \frac{1}{2}(1 - \sin 2\alpha) [/tex]
[tex] \frac{1}{2}(1 - \sin 2\alpha) = \frac{1}{2}(1 - \sin 2\alpha) [/tex]
