Toán Lớp 8: 7*sin(a)^2 + 5*cos(a)^2 = 13 /2 -

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Toán Lớp 8: 7sin(a)^2 + 5cos(a)^2 = 13 /2

Nhiên Tháng Một 18, 2023 Toán học 1 Comment 0 views

Toán Lớp 8: 7*sin(a)^2 + 5*cos(a)^2 = 13 /2

Comments ( 1 )

minhtamnguyet88
18 Tháng Một, 2023 at 3:19 sáng

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7\sin(a)^2+5\cos(a)^2=13/2

<=> 7\sin(a)^2+5[1-\sin(a)^2]=13/2

<=> 7\sin(a)^2+5-5\sin(a)^2=13/2

<=> 2\sin(a)^2+5=13/2

<=> 2\sin(a)^2=13/2-5

<=> 2\sin(a)^2=3/2

<=> \sin(a)^2=3/4

<=> \sin(a)=+-(\sqrt{3})/4

<=>\(\left[ \begin{array}{l}\sin(a)=-\dfrac{\sqrt{3}}{2}\\\sin(a)=\dfrac{\sqrt{3}}{2}\end{array} \right.\)

<=>\(\left[ \begin{array}{l}\begin{cases}a=\dfrac{5\pi}{3}+2k\pi\\a=\dfrac{4\pi}{3}+2k\pi\end{cases}\\\begin{cases}a=\dfrac{\pi}{3}+2k\pi\\a=\dfrac{2\pi}{3}+2k\pi\end{cases}\end{array} \right.\)

<=>\(\left[ \begin{array}{l}a=\dfrac{\pi}{3}+k\pi\\a=\dfrac{2\pi}{3}+k\pi\end{array} \right. k\in\mathbb{Z}\)

<=>\(a=\begin{cases}\dfrac{\pi}{3}+k\pi\\\dfrac{2\pi}{3}+k\pi\end{cases}, k\in\mathbb{Z}\)

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