Se tg(x+y)= 33 e tgx= 3, determine o valor de tg2y.
a)91/6
b)18/50
c)60/91
d)48/78
e)31/62
Alguem por favor pode me ajudar ?
Soluções para a tarefa
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Boa tarde!
Solução!
![33=\dfrac{3+tg_{y} }{1-3tg_{y} }\\\\\\\
33(1- 3tg_{y})=3+tg_{y} \\\\\\
33-99tg_{y}=3+tg_{y} \\\\\\
33-3=99tg_{y}+tg_{y} \\\\\\
30=100tg_{y}\\\\\\\
\boxed{tg_{y}= \dfrac{30}{100} }](https://tex.z-dn.net/?f=+33%3D%5Cdfrac%7B3%2Btg_%7By%7D+%7D%7B1-3tg_%7By%7D+%7D%5C%5C%5C%5C%5C%5C%5C%0A33%281-+3tg_%7By%7D%29%3D3%2Btg_%7By%7D+%5C%5C%5C%5C%5C%5C%0A33-99tg_%7By%7D%3D3%2Btg_%7By%7D+%5C%5C%5C%5C%5C%5C%0A33-3%3D99tg_%7By%7D%2Btg_%7By%7D+%5C%5C%5C%5C%5C%5C%0A30%3D100tg_%7By%7D%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Btg_%7By%7D%3D+%5Cdfrac%7B30%7D%7B100%7D+%7D "33=\dfrac{3+tg_{y} }{1-3tg_{y} }\\\\\\\
33(1- 3tg_{y})=3+tg_{y} \\\\\\
33-99tg_{y}=3+tg_{y} \\\\\\
33-3=99tg_{y}+tg_{y} \\\\\\
30=100tg_{y}\\\\\\\
\boxed{tg_{y}= \dfrac{30}{100} }")
Lembrando do arco duplo!
![\boxed{tg_{2y}= \dfrac{tg_{y}+ tg_{y}}{1-(tg_{y})^{2} }}\\\\\\\\
tg_{2y}= \dfrac{0,3+ 0,3}{1-(0,3)^{2} }\\\\\\\
tg_{2y}= \dfrac{0,6}{1-0,09}\\\\\\\ tg_{2y}= \dfrac{0,6}{0,91}\\\\\\\](https://tex.z-dn.net/?f=%5Cboxed%7Btg_%7B2y%7D%3D+%5Cdfrac%7Btg_%7By%7D%2B+tg_%7By%7D%7D%7B1-%28tg_%7By%7D%29%5E%7B2%7D+%7D%7D%5C%5C%5C%5C%5C%5C%5C%5C%0A++tg_%7B2y%7D%3D+%5Cdfrac%7B0%2C3%2B+0%2C3%7D%7B1-%280%2C3%29%5E%7B2%7D+%7D%5C%5C%5C%5C%5C%5C%5C%0A+tg_%7B2y%7D%3D+%5Cdfrac%7B0%2C6%7D%7B1-0%2C09%7D%5C%5C%5C%5C%5C%5C%5C%C2%A0tg_%7B2y%7D%3D+%5Cdfrac%7B0%2C6%7D%7B0%2C91%7D%5C%5C%5C%5C%5C%5C%5C "\boxed{tg_{2y}= \dfrac{tg_{y}+ tg_{y}}{1-(tg_{y})^{2} }}\\\\\\\\
tg_{2y}= \dfrac{0,3+ 0,3}{1-(0,3)^{2} }\\\\\\\
tg_{2y}= \dfrac{0,6}{1-0,09}\\\\\\\ tg_{2y}= \dfrac{0,6}{0,91}\\\\\\\")
Transformando os decimais em fração!
![tg_{2y}= \dfrac{6}{ \dfrac{10}{ \dfrac{91}{100} } }\\\\\\\
tg_{2y}= \dfrac{3}{5} \times \dfrac{100}{91}\\\\\\\
tg_{2y}= \dfrac{3}{1} \times \dfrac{20}{91} \\\\\\\
tg_{2y}= \dfrac{60}{91}](https://tex.z-dn.net/?f=tg_%7B2y%7D%3D+%5Cdfrac%7B6%7D%7B+%5Cdfrac%7B10%7D%7B+%5Cdfrac%7B91%7D%7B100%7D+%7D+%7D%5C%5C%5C%5C%5C%5C%5C%0Atg_%7B2y%7D%3D++%5Cdfrac%7B3%7D%7B5%7D+%5Ctimes++%5Cdfrac%7B100%7D%7B91%7D%5C%5C%5C%5C%5C%5C%5C%0Atg_%7B2y%7D%3D++%5Cdfrac%7B3%7D%7B1%7D+%5Ctimes++%5Cdfrac%7B20%7D%7B91%7D+%5C%5C%5C%5C%5C%5C%5C%0Atg_%7B2y%7D%3D++%5Cdfrac%7B60%7D%7B91%7D%0A "tg_{2y}= \dfrac{6}{ \dfrac{10}{ \dfrac{91}{100} } }\\\\\\\
tg_{2y}= \dfrac{3}{5} \times \dfrac{100}{91}\\\\\\\
tg_{2y}= \dfrac{3}{1} \times \dfrac{20}{91} \\\\\\\
tg_{2y}= \dfrac{60}{91}")
Boa tarde!
Bons estudos!
Solução!
Lembrando do arco duplo!
Transformando os decimais em fração!
Boa tarde!
Bons estudos!
lulua321:
vlw me ajudou muito !
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