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Calculati: tg²30+ctg²45= ??

Răspuns :

tg30°=1/√3  ;tg²30°=(1/√3)²=1/3
ctg45°=1  ;ctg²45°=1²=1

tg²30°+ctg²45°=1/3+1=4/3
tg 30=[tex] \frac{ \sqrt{3} }{3} [/tex] => tg^2 30 = ([tex] \frac{ \sqrt{3} }{3} [/tex])^2=[tex] \frac{3}{9} [/tex]=[tex] \frac{1}{3} [/tex]

ctg 45=1=>ctg^2 45=1^2=1

[tex] tg^{2} 30+ ctg^{30} = \frac{1}{3}+1= \frac{4}{3} [/tex]