\(pt\Leftrightarrow\cos\frac{x}{4}\sin x+\cos x+\sin\frac{x}{4}\cos x=3\left(\sin^2x+\cos^2x\right)=3\)
Mà \(\sin\alpha;\text{ }\cos\alpha\le1\forall\alpha\)
\(\Rightarrow\cos\frac{x}{4}.\sin x\le1.1;\text{ }\sin\frac{x}{4}.\cos x\le1.1;\text{ }\cos x\le1\forall x\)
\(\Rightarrow\cos\frac{x}{4}.\sin x+\sin\frac{x}{4}.\cos x+\cos x\le3\text{ }\forall x\)
Dấu "=" xảy ra khi \(\cos x=1;\text{ }\cos\frac{x}{4}.\sin x=1;\text{ }\cos x.\sin\frac{x}{4}=1\)
\(\Leftrightarrow\cos x=1;\text{ }\sin\frac{x}{4}=1;\text{ }\cos\frac{x}{4}.\sin x=1\)
Pt trên vô nghiệm do \(\cos x=1\text{ thì }\sin x=0\Rightarrow\cos\frac{x}{4}.\sin x=0\)
Vậy phương trình đã cho vô nghiệm.
