14)\(cos^2\left(\dfrac{\pi}{3}+x\right)+4cos\left(\dfrac{\pi}{6}-x\right)=4\)
\(\Leftrightarrow-sin^2\left(\dfrac{\pi}{3}+x\right)+1+4.sin\left(\dfrac{\pi}{3}+x\right)=4\)
\(\Leftrightarrow-sin^2\left(\dfrac{\pi}{3}+x\right)+4sin\left(\dfrac{\pi}{3}+x\right)-3=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sin\left(\dfrac{\pi}{3}+x\right)=3\left(vn\right)\\sin\left(\dfrac{\pi}{3}+x\right)=1\end{matrix}\right.\)\(\Rightarrow x=\dfrac{\pi}{6}+k2\pi,k\in Z\)
Vậy...
12) ĐKXĐ: cosx , sinx≠0
pt <=> (cosx + 1) + ( sinx + 1) +\(\dfrac{1+cosx}{sinx}\)+ \(\dfrac{1+sinx}{cosx}\)
=0
<=> (cosx + 1 ) ( 1+ \(\dfrac{1}{sinx}\) ) + ( sinx+1)(1 + \(\dfrac{1}{cosx}\) ) = 0
<=> ( cosx + 1) ( sinx + 1) ( \(\dfrac{1}{sinx}\) + \(\dfrac{1}{cosx}\) ) = 0
<=> cos x = -1
hoặc sinx = -1
hoặc sinx + cos x = 0
