Odpowiedź:
[tex]\displaystyle tg\alpha= \frac{\sqrt{8} }{8} \\\frac{cos\alpha }{\frac{sin\alpha }{cos\alpha }-\sqrt{8} } +\frac{\sqrt{8}sin\alpha }{\sqrt{8}-\frac{sin\alpha }{cos\alpha } } =\frac{cos\alpha }{tg\alpha -\sqrt{8} } -\frac{\sqrt{8}sin\alpha }{tg\alpha -\sqrt{8} } =\\\frac{cos\alpha -\sqrt{8} sin\alpha/:cos\alpha }{tg\alpha -\sqrt{8} /:cos\alpha } =\frac{1 -\sqrt{8} tg\alpha }{\frac{tg\alpha }{cos\alpha } -\frac{\sqrt{8} }{cos\alpha } } =[/tex]
[tex]\displaystyle= \frac{1-\sqrt{8} \cdot\frac{\sqrt{8} }{8} }{\frac{tg\alpha }{cos\alpha } -\frac{\sqrt{8} }{cos\alpha }} =\frac{1-1}{\frac{tg\alpha }{cos\alpha } -\frac{\sqrt{8} }{cos\alpha }} =0[/tex]
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Odpowiedź:
[tex]\displaystyle tg\alpha= \frac{\sqrt{8} }{8} \\\frac{cos\alpha }{\frac{sin\alpha }{cos\alpha }-\sqrt{8} } +\frac{\sqrt{8}sin\alpha }{\sqrt{8}-\frac{sin\alpha }{cos\alpha } } =\frac{cos\alpha }{tg\alpha -\sqrt{8} } -\frac{\sqrt{8}sin\alpha }{tg\alpha -\sqrt{8} } =\\\frac{cos\alpha -\sqrt{8} sin\alpha/:cos\alpha }{tg\alpha -\sqrt{8} /:cos\alpha } =\frac{1 -\sqrt{8} tg\alpha }{\frac{tg\alpha }{cos\alpha } -\frac{\sqrt{8} }{cos\alpha } } =[/tex]
[tex]\displaystyle= \frac{1-\sqrt{8} \cdot\frac{\sqrt{8} }{8} }{\frac{tg\alpha }{cos\alpha } -\frac{\sqrt{8} }{cos\alpha }} =\frac{1-1}{\frac{tg\alpha }{cos\alpha } -\frac{\sqrt{8} }{cos\alpha }} =0[/tex]