Question

se tg(x+y)=33 e tgx=3 determine o valor de tg 2y

Answer 1

$tg (x + y) = (tg x + tg y) / (1 - tgx*tgy)$
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Como tg (x + y) = 33:

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