27.
\(cos\left(\dfrac{x}{2}+15^0\right)=sinx\)
\(\Leftrightarrow cos\left(\dfrac{x}{2}+15^0\right)=cos\left(90^0-x\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{x}{2}+15^0=90^0-x+k360^0\\\dfrac{x}{2}+15^0=x-90^0+k360^0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=50^0+k240^0\\x=210^0+k720^0\end{matrix}\right.\)
Với \(k=1\Rightarrow x=50^0+240^0=290^0\)
28.
\(sin\left(x-\dfrac{\pi}{4}\right)\ne0\)
\(\Leftrightarrow x-\dfrac{\pi}{4}\ne k\pi\)
\(\Leftrightarrow x\ne\dfrac{\pi}{4}+k\pi\)
29.
\(\Leftrightarrow cos\left(x+\dfrac{\pi}{3}\right)=\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{\pi}{3}=\dfrac{\pi}{4}+k2\pi\\x+\dfrac{\pi}{3}=-\dfrac{\pi}{4}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{12}+k2\pi\\x=-\dfrac{7\pi}{12}+k2\pi\end{matrix}\right.\)
\(\Rightarrow x=\left\{\dfrac{17\pi}{12};\dfrac{23\pi}{12}\right\}\)
30.
Pt \(2sinx+3cosx=1\) có \(2^2+3^2>1^2\) nên có nghiệm
31.
Hàm \(y=tan\left(kx\right)\) tuần hoàn với chu kì \(T=\dfrac{\pi}{\left|k\right|}\)
Nên hàm đã cho tuần hoàn với chu kì \(T=\dfrac{\pi}{2}\)
32.
\(sinx\le1\Rightarrow y\le1+2.1=3\)
Dấu "=" xảy ra khi \(sinx=1\)
\(\Leftrightarrow x=\dfrac{\pi}{2}+k2\pi\)
