wykaż że jeśli a jest kątem ostrym i (1/1-cos - 1/1+cos)=4/sin to tg=0,5.... Question from @pau19

pau19 @pau19

November 2018 2 20 Report

wykaż że jeśli a jest kątem ostrym i (1/1-cos - 1/1+cos)=4/sin to tg=0,5

mateusz04081999

=4sin +0,5 sin a wynik se obliczysz

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Heinkel1

$(\frac{1}{1-cos\alpha}-\frac{1}{1+cos\alpha})=\frac{4}{sin\alpha}\\ \frac{1+cos\alpha-1+cos\alpha}{(1-cos\alpha)(1+cos\alpha)}=\frac{4}{sin\alpha}\\ \frac{2cos\alpha}{1-cos^{2}\alpha}=\frac{4}{sin\alpha}\\ \frac{2cos\alpha}{sin^{2}\alpha}=\frac{4}{sin\alpha}\\ 4sin^{2}\alpha=2sin\alpha cos\alpha\\ 2sin\alpha=cos\alpha\\ sin\alpha=\frac{1}{2}cos\alpha\\ \frac{sin\alpha}{cos\alpha}=\frac{1}{2}\\ tg\alpha=\frac{1}{2}$

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