a.
\(sinx=sin\left(-30^0\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-30^0+k360^0\\x=210^0+k360^0\end{matrix}\right.\)
b.
\(tan3x=tan\left(-\dfrac{\pi}{6}\right)\)
\(\Leftrightarrow3x=-\dfrac{\pi}{6}+k\pi\)
\(\Leftrightarrow x=-\dfrac{\pi}{18}+k\pi3\)
c.
\(cosx=cos\left(\dfrac{\pi}{5}\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{5}+k2\pi\\x=-\dfrac{\pi}{5}+k2\pi\end{matrix}\right.\)
d.
\(cotx=cot\left(-127^0\right)\)
\(\Leftrightarrow x=-127^0+k180^0\)
e.
\(sin\left(\dfrac{\pi}{3}+2x\right)=sin\left(\dfrac{19\pi}{3}-2x\right)\)
\(\Leftrightarrow sin\left(\dfrac{\pi}{3}+2x\right)=sin\left(\dfrac{\pi}{3}-2x\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{\pi}{3}+2x=\dfrac{\pi}{3}-2x+k2\pi\\\dfrac{\pi}{3}+2x=\dfrac{\pi}{6}+2x+k2\pi\left(vn\right)\end{matrix}\right.\)
\(\Leftrightarrow x=\dfrac{k\pi}{2}\)
f.
\(cos\left(4x+37^0\right)=cos\left(397^0+4x\right)\)
\(\Leftrightarrow cos\left(4x+37^0\right)=cos\left(360^0+37^0+4x\right)\)
\(\Leftrightarrow cos\left(4x+37^0\right)=cos\left(4x+37^0\right)\) (luôn đúng)
Vậy nghiệm của pt đã cho là \(x\in R\)
