Question

Seja a tg a = 1/3, então o valor de Tg(45 + a) é igual a:
A) 1
B) 2
C) 3
D) 4

Answer 1

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$\sf{tg(45^\circ+\alpha)=\dfrac{tg(45^\circ)+tg(\alpha)}{1-tg(45^\circ)\cdot tg(\alpha)}}\\\sf{tg(45^\circ+\alpha)=\dfrac{1+\frac{1}{3}}{1-1\cdot\frac{1}{3}}}\\\sf{tg(45^\circ+\alpha)=\dfrac{1+\frac{1}{3}}{1-\frac{1}{3}}}\\\sf{tg(45^\circ+\alpha)=\dfrac{\frac{4}{3}}{\dfrac{2}{3}}}\\\sf{tg(45^\circ+\alpha)=\dfrac{\diagup\!\!\!4^2}{\diagup\!\!\!3}\cdot\dfrac{\diagup\!\!\!3}{\diagup\!\!\!2}=2\checkmark}$