Question

Simplificando a expressão trigonométrica abaixo, obtemos

a) tan a . tan b
b) cot a. cot b
c) tan (a + b)
d) cot (a + b)
e) tan a . cot b

Answer 1

$\Large\boxed{\begin{array}{l}\sf\dfrac{tg(a)+tg(b)}{cot(a)+cot(b)}=\dfrac{\frac{sen(a)}{cos(a)}+\frac{sen(b)}{cos(b)}}{\frac{cos(a)}{sen(a)}+\frac{cos(b)}{sen(b)}}\\\\\sf\dfrac{tg(a)+tg(b)}{cot(a)+cot(b)}=\dfrac{\frac{sen(a)\cdot cos(b)+sen (b)\cdot cos(a)}{cos(a)\cdot cos(b)}}{\frac{sen(b)\cdot cos(a)+sen (a)\cdot cos(b)}{sen(a)\cdot sen(b)}}\end{array}}$

$\boxed{\begin{array}{l}\sf\dfrac{tg(a)+tg(b)}{cot(a)+cot(b)}=\\\\\sf\dfrac{sen(a)\cdot cos(b)+sen (b)\cdot cos(a)}{cos(a)\cdot cos(b)}\cdot\dfrac{sen(a)\cdot sen(b)}{sen(b)\cdot cos(a)+sen(a)\cdot cos(b)}\\\\\sf\dfrac{sen(a+b)}{cos(a)\cdot cos(b)}\cdot\dfrac{sen(a)\cdot sen(b)}{sen(b+a)}\\\\\sf\dfrac{tg(a)+tg(b)}{cot(a)+cot(b)}=\dfrac{\diagup\!\!\!sen\diagup\!\!\!\!\!(a+\diagup\!\!\!\!b)}{\diagup\!\!\!\!sen\diagup\!\!(a+\diagup\!\!\!\!\!b)}\cdot\dfrac{sen(a)}{cos(a)}\cdot\dfrac{sen(b)}{cos(b)}\end{array}}$

$\Large\boxed{\begin{array}{l}\huge\boxed{\boxed{\boxed{\boxed{\sf\dfrac{tg(a)+tg(b)}{cot(a)+cot(b)}= tg(a)\cdot tg(b)}}}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~a}}}}\end{array}}$