Odpowiedź:
tg α - ctg α = [tex]\frac{5}{6}[/tex]
Podnosimy obustronnie do kwadratu:
[tex]tg^2\alpha - 2 tg \alpha *ctg \alpha + ctg^2\alpha = \frac{25}{36}[/tex]
[tex]tg^2 \alpha -2*1 + ctg^2\alpha = \frac{25}{36}[/tex]
[tex]tg^2\alpha + ctg^2\alpha = \frac{25}{36} + \frac{72}{36} = \frac{97}{36}[/tex]
Podnosimy ponownie do 2 potęgi:
[tex]tg^4\alpha + 2*tg^2\alpha *ctg^2\alpha + ctg^4\alpha = \frac{9 409}{1 296}[/tex]
[tex]tg^4\alpha + 2*( tg\alpha *ctg\alpha )^2 + ctg^4\alpha = \frac{9 409}{1 296}[/tex]
[tex]tg^4\alpha + ctg^4\alpha = \frac{9 409}{1 296} -2 = \frac{9 409}{1 296} - \frac{2592}{1 296} =[/tex] [tex]\frac{6 817}{1 296} = 5 \frac{337}{ 1 296}[/tex]
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Szczegółowe wyjaśnienie:
