Question

\(\frac{3\left(cos2x+cot2x\right)}{cot2x-cos2x}=4sin\left(\frac{\pi}{4}+x\right)cos\left(\frac{\pi}{4}-x\right)\)

​\(\frac{3\left(cos2x+cot2x\right)}{cot2x-cos2x}=4sin\left(\frac{\pi}{4}+x\right)cos\left(\frac{\pi}{4}-x\right)\)​

\(\frac{3\left(cos2x+cot2x\right)}{cot2x-cos2x}=4sin\left(\frac{\pi}{4}+x\right)cos\left(\frac{\pi}{4}-x\right)\)

Answer 1

ĐKXĐ: ...

\(\frac{3\left(cos2x+\frac{cos2x}{sin2x}\right)}{\frac{cos2x}{sin2x}-cos2x}=2sin\left(\frac{\pi}{2}\right)+2sin2x\)

\(\Leftrightarrow\frac{3\left(sin2x+1\right)}{1-sin2x}=2+2sin2x\)

\(\Leftrightarrow\left(1+sin2x\right)\left(\frac{3}{1-sin2x}-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}sin2x=-1\\sin2x=-\frac{1}{2}\end{matrix}\right.\)

\(\Leftrightarrow...\)