d)
PT \(\Leftrightarrow sin^2x-3sinx.cosx=sin^2x+cos^2x\)
\(\Leftrightarrow cos^2x+3sinx.cosx=0\)
\(\Leftrightarrow cosx\left(cosx+3sinx\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\cosx=-3sinx\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\tanx=-\dfrac{1}{3}\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\x=arc.tan\left(-\dfrac{1}{3}\right)+k\pi\end{matrix}\right.\) (\(k\in Z\))
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