cos(x+30°)+2cos^215°=1

Đáp án:

\(\left[ \begin{array}{l}x=120°+k.360\\x=-180°+k.360\end{array} \right.\)  \((k \epsilon Z)\)

Giải thích các bước giải:

 \(\cos(x+30°)+2\cos^{2} 15°=1\)

\(\Leftrightarrow \cos (x+30°)+2\cos^{2} 15°-1=0\)

\(\Leftrightarrow \cos(x+30°)+\cos 30°=0\)

\(\Leftrightarrow \cos(x+30°)=-\dfrac{\sqrt{3}}{2}\)

\(\Leftrightarrow \cos(x+30°)=\cos(150°)\)

\(\Leftrightarrow \) \(\left[ \begin{array}{l}x+30°=150°+k.360\\x+30°=-150°+k.360\end{array} \right.\)  \((k \epsilon Z)\)

\(\Leftrightarrow \) \(\left[ \begin{array}{l}x=120°+k.360\\x=-180°+k.360\end{array} \right.\)  \((k \epsilon Z)\)