\(10cos^2x-5sinx.cosx+3sin^2x=4\)
\(\Leftrightarrow20cos^2x-10-10sinx.cosx+6sin^2x-3+5=0\)
\(\Leftrightarrow7cos2x-5sin2x=-5\)
\(\Leftrightarrow\sqrt{74}\left(\dfrac{7}{\sqrt{74}}cos2x-\dfrac{5}{\sqrt{74}}sin2x\right)=-5\)
\(\Leftrightarrow cos\left(2x+arccos\dfrac{7}{\sqrt{74}}\right)=-\dfrac{5}{\sqrt{74}}\)
\(\Leftrightarrow2x+arccos\dfrac{7}{\sqrt{74}}=\pm arccos\left(-\dfrac{5}{\sqrt{74}}\right)+k2\pi\)
\(\Leftrightarrow x=-\dfrac{1}{2}arccos\dfrac{7}{\sqrt{74}}\pm\dfrac{1}{2}arccos\left(-\dfrac{5}{\sqrt{74}}\right)+k\pi\)
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