преобразуване

[uhu]

sin4 \alpha - cos4\alpha =(sin2\alpha + cos2\alpha )на 2 - 2sin2\alpha .cos2\alpha ??

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[ObsCure]

Грешен раздел и неразбираемо условие.

[b1ck0]

[tex] sin4 \alpha - cos4\alpha = (sin2\alpha + cos2\alpha )^{2} - 2sin2\alpha .cos2\alpha [/tex]

[tex] sin4 \alpha - cos4\alpha = \underbrace{sin^{2}2\alpha + cos^{2}2\alpha}_{1} + \cancel{2sin2\alpha .cos2\alpha} - \cancel{2sin2\alpha .cos2\alpha} [/tex]

[tex] sin4 \alpha - cos4\alpha = 1 \Rightarrow sin4\alpha = 1, cos4\alpha = 0[/tex]

[tex] 4\alpha = \frac{\pi}{2} + k\pi \Rightarrow \alpha = \frac{\pi}{8} + \frac{k\pi}{4}[/tex]