Odpowiedź:
[tex]sin^2\alpha *tg^2\alpha - cos^2\alpha =\\[/tex] [tex]sin^2\alpha *\frac{sin^2\alpha }{cos^2\alpha } - \frac{cos^4\alpha }{cos^2\alpha } =[/tex]
= [tex]\frac{sin^4\alpha - cos^4\alpha }{cos^2\alpha } = \frac{(sin^2 \alpha - cos^2\alpha )*(sin^2\alpha + cos^2\alpha) }{cos^2\alpha } =[/tex]
= [tex]\frac{sin^2\alpha - cos^2\alpha }{cos^2\alpha } = tg^2\alpha - 1[/tex]
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1) x² = 3² + 4² = 9 + 16 = 25 ⇒ x = 5
sin α = [tex]\frac{3}{5}[/tex] [tex]cos \alpha = \frac{4}{5}[/tex] [tex]tg \alpha = \frac{3}{4}[/tex] [tex]ctg \alpha = \frac{4}{3}[/tex]
2) x² + 8² = 12² ⇒ x² = 144 - 64 = 80 = 16*5 ⇒ x = 4√5
[tex]sin \alpha = \frac{8}{12} = \frac{2}{3}[/tex] [tex]cos \alpha = \frac{4\sqrt{5} }{12} = \frac{\sqrt{5} }{3}[/tex] [tex]tg \alpha = \frac{8}{4\sqrt{5} } = \frac{2}{\sqrt{5} } = \frac{2\sqrt{5} }{5}[/tex] [tex]ctg \alpha = \frac{\sqrt{5} }{2}[/tex]
3) [tex]x^{2} +[/tex] [tex]8^2 = 17^2[/tex] ⇒ x² = 289 - 64 = 225 ⇒ x = 15
[tex]sin \alpha = \frac{15}{17}[/tex] [tex]cos \alpha = \frac{8}{17}[/tex] [tex]tg \alpha = \frac{15}{8}[/tex] [tex]ctg \alpha = \frac{8}{15}[/tex]
Szczegółowe wyjaśnienie:
