Question

Os valores de m para que se tenha simultaneamente
sen 0 = 1 + 4m e cos 0 = 1 + 2m são​

Answer 1

$\sf{sen^2(\theta)+cos^2(\theta)=1}\\\sf{(1+4m) ^2+(1+2m)^2=1}\\\sf{ \diagup\!\!\!\! 1+8m+16m^2+1+4m+4m^2-\diagup\!\!\!\!1=0}\\\sf{20m^2+12m+1}\\\sf{a=20~~~b=12~~~c=1}\\\sf{\Delta=b^2-4ac}\\\sf{\Delta=12^2-4\cdot20\cdot1}\\\sf{\Delta=144-80}\\\sf{\Delta=64}\\\sf{m=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\sf{m=\dfrac{-12\pm\sqrt{64}}{2\cdot20}}\\\sf{m=\dfrac{-12\pm8}{40}}\begin{cases}\sf{m_1=\dfrac{-12+8}{40}=\dfrac{-4}{40}=-\dfrac{1}{10}}\\\sf{m_2=\dfrac{-12-8}{40}=-\dfrac{20}{40}=-\dfrac{1}{2}}\end{cases}$

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