(ITA) - Tangente de arco metade.

por Betoneira de Natal Sex 18 Mar 2022, 23:08

(ITA) Sabendo que

(ITA) - Tangente de arco metade. Svg+xml;base64,<?xml version='1.0' encoding='UTF-8'?>
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, com

, assinale a opção que representa o valor de

a) 1/3
b) 1/4
c) 1/5
d) 1/6
e) 1/8

Resp.: Sem gabarito.

Como posso relacionar a primeira relação que ele me deu?
Consegui apenas desenvolver o que ele pede, que é a multiplicação dos arcos metades de tangente.

por **Giovana Martins** Sáb 19 Mar 2022, 07:15

[latex]\mathrm{2sin(\alpha +\beta )=sin(\alpha )+sin(\beta )\underset{Prostaf\acute{e}rese}{=\underbrace{\mathrm{2sin\left ( \frac{\alpha +\beta }{2} \right )cos\left ( \frac{\alpha -\beta }{2} \right )}}}}[/latex]

[latex]\mathrm{2sin(\alpha +\beta )cos\left ( \frac{a+\beta }{2} \right )=2sin\left ( \frac{\alpha +\beta }{2} \right )cos\left ( \frac{\alpha +\beta }{2} \right )cos\left ( \frac{\alpha -\beta }{2} \right )}[/latex]

[latex]\mathrm{2\cancel{\mathrm{sin(\alpha +\beta )}}cos\left ( \frac{a+\beta }{2} \right )=\cancel{\mathrm{sin(\alpha +\beta )}}cos\left ( \frac{\alpha -\beta }{2} \right )}[/latex]

[latex]\mathrm{2\left [ cos\left ( \frac{\alpha }{2} \right )cos\left ( \frac{\beta }{2} \right )-sin\left ( \frac{\alpha }{2} \right )sin\left ( \frac{\beta }{2} \right ) \right ]=cos\left ( \frac{\alpha }{2} \right )cos\left ( \frac{\beta }{2} \right )+sin\left ( \frac{\alpha }{2} \right )sin\left ( \frac{\beta }{2} \right )}[/latex]

[latex]\mathrm{cos\left ( \frac{\alpha }{2} \right )cos\left ( \frac{\beta }{2} \right )=3sin\left ( \frac{\alpha }{2} \right )sin\left ( \frac{\beta }{2} \right )\ \therefore \ tan\left ( \frac{\alpha }{2} \right )tan\left ( \frac{\beta }{2} \right )=\frac{1}{3}}[/latex]

por Betoneira de Natal Sáb 19 Mar 2022, 18:59

Olá Gi.

Adorei sua resolução, nunca q eu ia pensar nela kkkk.
Vlw de vdd.
Foi massa! Cool

por **Giovana Martins** Sáb 19 Mar 2022, 19:16

Oiii. De nada!!!

Eu demorei para enxergar aquela multiplicação dos dois lados da equação por cosseno. Tentei resolver ontem à noite e não consegui. Só consegui hoje cedo. Pelo menos para mim o que mais atrapalha na questão é essa multiplicação. Na pressão resolver a questão logo na prova isso deve ter atrapalhado bastante o pessoal.

Mas com certeza você pensaria. Conforme você vai treinando com muitas questões de níveis variados você fica com o olho mais "afiado".

por Betoneira de Natal Sáb 19 Mar 2022, 19:35

Ahh entendi.
Realmente, quando eu botei o olho nela n veio nada, nem 1 ideia sequer kkkk.

Eu tô tentando reforçar bem trigonometria pq eu tô bem ruim nela ainda.
Mas vamo q vamo!

Cool