Trygonometria

[avleyi]

Załóżmy, że \(\sin2 \alpha = \frac{2}{3}. \) Oblicz \(\sin^4 \alpha +\cos^4 \alpha. \)

[Jerry]

\(\sin^4 \alpha +\cos^4 \alpha=(\sin^2 \alpha +\cos^2 \alpha)^2-2\sin^2\alpha\cos^2\alpha=\\ \quad=1^2-{1\over2}\cdot(\sin2\alpha)^2=1-{1\over2}\cdot{2\over3}={2\over3}\)

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