Question

Dados Tg a = 2/3 e Tg b = 3/4. Qual o valor da Tg(a+b) ?​

Answer 1

Resposta:

Soma  de dois arcos

$tg(a+b)=\dfrac{tg(a)+tg(b)}{1-tg(a).tg(b)}$

Sendo:

Tg(a )= 2/3 e Tg(b )= 3/4

$tg(a+b)=\dfrac{\dfrac{2}{3}+\dfrac{3}{4}}{1-\dfrac{2}{3}.(\dfrac{3}{4}}\\ \\ \\ tg(a+b)=\dfrac{\dfrac{8+9}{12}}{1-\dfrac{6}{12}}}\\ \\ \\ tg(a+b)=\dfrac{\dfrac{17}{12}}{\dfrac{12-6}{12}}\\ \\ \\ tg(a+b)=\dfrac{17}{12}\div\dfrac{6}{12}\\ \\ \\ tg(a+b)=\dfrac{17}{\not12}\times\dfrac{\not12}{6}\\ \\ \\\boxed{\ tg(a+b)=\dfrac{17}{6}}$