Question

Consider cot(2x).
Uma fórmula equivalente para cot(2x) é:

( ) (1/2)*(cot(x)-tan(x))
( ) cot(x)+tan(x)
( ) -(1/2)*(tan(x)-cot(x))

Answer 1

Sabemos que :

$\displaystyle \sf Tan(2x) = \frac{2Tan(x) }{1-Tan^2(x)} \\\\\ Da{\'i} } : \\\\ Cot(2x) = \frac{1}{Tan(2x)} \\\\\\ Cot(2x) = \frac{1}{\displaystyle \frac{2Tan(x) }{1-Tan^2(x)} } \\\\\\ Cot(2x) = \frac{1-Tg^2(x)}{2Tan(x)} \\\\\\ Cot(2x) = \frac{1}{2Tan(x)} -\frac{Tan^2(x)}{2Tan(x)} \\\\\\ Cot(2x) = \frac{1}{2}\cdot Cot(x) - \frac{1}{2}\cdot Tan(x) \\\\\\ \boxed{\sf \ Cot(2x) = \frac{1}{2}\cdot \left [Cot(x) - Tan(x) \right] \ }\checkmark$