74.
\(2cos\left(x+45^o\right)-\sqrt{2}=0\)
\(\Leftrightarrow cos\left(x+45^o\right)=\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow x+45^o=\pm45^o+k.360^o\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k.360^o\\x=-90^o+k.360^o\end{matrix}\right.\)
75.
\(tan4x=-\dfrac{1}{3}\)
\(\Leftrightarrow4x=arctan\left(-\dfrac{1}{3}\right)+k\pi\)
\(\Leftrightarrow x=\dfrac{1}{4}arctan\left(-\dfrac{1}{3}\right)+\dfrac{k\pi}{4}\)
\(x=\dfrac{1}{4}arctan\left(-\dfrac{1}{3}\right)+\dfrac{k\pi}{4}< 0\Leftrightarrow k< -\dfrac{arctan\left(-\dfrac{1}{3}\right)}{\pi}\approx0,1\Rightarrow k=0\)
\(\Rightarrow x=\dfrac{1}{4}arctan\left(-\dfrac{1}{3}\right)\)
Làm lại 76, lúc này làm sai.
\(x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}>0\Leftrightarrow k>-\dfrac{1}{2}\Rightarrow k=0\Rightarrow x=\dfrac{\pi}{4}\)
\(x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}< 0\Leftrightarrow k< -\dfrac{1}{2}\Rightarrow k=-1\Rightarrow x=-\dfrac{\pi}{4}\)
