Question

Se cot x = – 4 , qual o valor de tan 2x???

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\mathsf{cotg\:x = \dfrac{1}{tg\:x}}$

$\mathsf{\dfrac{1}{tg\:x} = -4}$

$\boxed{\boxed{\mathsf{tg\:x = -\dfrac{1}{4}}}}$

$\mathsf{tg\:2x = \dfrac{2\:tg\:x}{1 - tg^2\:x}}$

$\mathsf{tg\:2x = \dfrac{2 \times -\dfrac{1}{4}}{1 - (-\dfrac{1}{4})^2}}$

$\mathsf{tg\:2x = \dfrac{-\dfrac{1}{2}}{1 - \dfrac{1}{16}}}$

$\mathsf{tg\:2x = -\dfrac{1}{2} \times \dfrac{16}{15}}}$

$\mathsf{tg\:2x = -\dfrac{16}{30}}$

$\boxed{\boxed{\mathsf{tg\:2x = -\dfrac{8}{15}}}}$