Matemática, perguntado por enzolc31, 7 meses atrás

Alguem pra tentar me ajudar ?

Estou com uma duvida

Anexos:

Soluções para a tarefa

Respondido por HoundSpacePigXels
2

Resposta:

-1

Explicação passo-a-passo:

\frac{sin\left(120\right)\cdot \:tan\left(240\right)}{tan\left(315\right)-cos\left(300\right)}\\\mathrm{Usar\:a\:seguinte\:identidade}:\quad \cos \left(x\right)=\sin \left(90^{\circ \:}-x\right)\\\cos \left(300^{\circ \:}\right)=\sin \left(90^{\circ \:}-300^{\circ \:}\right)\\\frac{\sin \left(120^{\circ \:}\right)\tan \left(240^{\circ \:}\right)}{\tan \left(315^{\circ \:}\right)-\sin \left(90^{\circ \:}-300^{\circ \:}\right)}\\

\frac{\sin \left(120^{\circ \:}\right)\tan \left(240^{\circ \:}\right)}{\tan \left(315^{\circ \:}\right)-\sin \left(-210^{\circ \:}\right)}\\\mathrm{Utilizar\:a\:seguinte\:propriedade:}\:\sin \left(-x\right)=-\sin \left(x\right)\\\sin \left(-210^{\circ \:}\right)=-\sin \left(210^{\circ \:}\right)\\\frac{\sin \left(120^{\circ \:}\right)\tan \left(240^{\circ \:}\right)}{\tan \left(315^{\circ \:}\right)-\left(-\sin \left(210^{\circ \:}\right)\right)}\\

\frac{\sin \left(120^{\circ \:}\right)\tan \left(240^{\circ \:}\right)}{\tan \left(315^{\circ \:}\right)+\sin \left(210^{\circ \:}\right)}\\\tan \left(240^{\circ \:}\right)=\tan \left(60^{\circ \:}\right)\\\frac{\sin \left(120^{\circ \:}\right)\tan \left(60^{\circ \:}\right)}{\tan \left(315^{\circ \:}\right)+\sin \left(210^{\circ \:}\right)}\\\tan \left(315^{\circ \:}\right)=\tan \left(135^{\circ \:}\right)\\

\frac{\sin \left(120^{\circ \:}\right)\tan \left(60^{\circ \:}\right)}{\tan \left(135^{\circ \:}\right)+\sin \left(210^{\circ \:}\right)}\\\sin \left(120^{\circ \:}\right)=\frac{\sqrt{3}}{2}\\\mathrm{Utilizar\:a\:seguinte\:identidade\:trivial}:\quad \tan \left(60^{\circ \:}\right)=\sqrt{3}\\\tan \left(315^{\circ \:}\right)=-1\\\sin \left(210^{\circ \:}\right)=-\frac{1}{2}\\\frac{\frac{\sqrt{3}}{2}\sqrt{3}}{-1-\frac{1}{2}}=-1


enzolc31: Ahh, passei perto
enzolc31: obg por me ajudar !
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