obliczyć sinusa z wyrażenia
: 20 lut 2010, o 08:43
\(\displaystyle{ sin ^{4} \alpha +cos ^{4} \alpha = 4sin ^{ 2 } - \frac{1}{2} sin ^{2} 2 \alpha}\)
\(\displaystyle{ sin ^{4} \alpha +cos ^{4} \alpha = 4sin ^{ 2 } \alpha - \frac{1}{2} sin ^{2} 2 \alpha
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(sin ^{2} \alpha + cos ^{2} \alpha )^2 -2sin ^{2} \alpha \cdot cos ^{2} \alpha = 4sin ^{2} \alpha - 0,5(2 sin \alpha \cdot cos \alpha )^{2}
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1 - 2sin ^{2} \alpha \cdot cos ^{2} \alpha = 4sin ^{2} \alpha - 2sin ^{2} \alpha \cdot cos ^{2} \alpha
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4sin ^{2} \alpha= 1
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sin ^{2} \alpha= 0,25
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sin \alpha= 0,5 \ \ \vee \ \ sin \alpha= -0,5}\)