Resposta :
[tex]tg (x + y) = (tg x + tg y) / (1 - tgx*tgy)[/tex]
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Como tg (x + y) = 33:
[tex](tg x + tg y) / (1 - tgx*tgy) = tg(x + y)[/tex]
[tex](tg x + tg y) / (1 - tgx*tgy) = 33[/tex]
[tex](tg x + tg y) = 33(1 - tgx*tgy)[/tex]
[tex]3 + tgy = 33(1 - 3*tgy)[/tex]
[tex]3 + tgy = 33 - 99tgy[/tex]
[tex]tgy + 99tgy = 33 - 3[/tex]
[tex]100tgy = 30[/tex]
[tex]tgy = 30/100[/tex]
[tex]tgy=3/10[/tex]
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[tex]tg (x + y) = (tg x + tg y) / (1 - tgx*tgy)[/tex]
[tex]tg (y + y) = (tg y + tg y) / (1 - tgy*tgy)[/tex]
[tex]tg 2y = 2tgy/(1 - tg^{2}y)[/tex]
[tex]tg2y = 2*[3/10] / (1 - [3/10]^{2})[/tex]
[tex]tg2y = (3 / 5) / (1 - [9/100])[/tex]
[tex]tg2y = (3/5) / ([100/100] - [9/100])[/tex]
[tex]tg2y = (3/5) / ([100-9]/100)[/tex]
[tex]tg2y = (3/5) / (91/100)[/tex]
[tex]tg2y = (3/5) * (100/91)[/tex]
[tex]tg2y = (3/1)*(20/91)[/tex]
[tex]tg2y = 60/91[/tex]
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Como tg (x + y) = 33:
[tex](tg x + tg y) / (1 - tgx*tgy) = tg(x + y)[/tex]
[tex](tg x + tg y) / (1 - tgx*tgy) = 33[/tex]
[tex](tg x + tg y) = 33(1 - tgx*tgy)[/tex]
[tex]3 + tgy = 33(1 - 3*tgy)[/tex]
[tex]3 + tgy = 33 - 99tgy[/tex]
[tex]tgy + 99tgy = 33 - 3[/tex]
[tex]100tgy = 30[/tex]
[tex]tgy = 30/100[/tex]
[tex]tgy=3/10[/tex]
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[tex]tg (x + y) = (tg x + tg y) / (1 - tgx*tgy)[/tex]
[tex]tg (y + y) = (tg y + tg y) / (1 - tgy*tgy)[/tex]
[tex]tg 2y = 2tgy/(1 - tg^{2}y)[/tex]
[tex]tg2y = 2*[3/10] / (1 - [3/10]^{2})[/tex]
[tex]tg2y = (3 / 5) / (1 - [9/100])[/tex]
[tex]tg2y = (3/5) / ([100/100] - [9/100])[/tex]
[tex]tg2y = (3/5) / ([100-9]/100)[/tex]
[tex]tg2y = (3/5) / (91/100)[/tex]
[tex]tg2y = (3/5) * (100/91)[/tex]
[tex]tg2y = (3/1)*(20/91)[/tex]
[tex]tg2y = 60/91[/tex]