Câu 4: sin 2x=0=>\(2x=k\pi\) =>\(x=\frac{k\pi}{2}\) \(x\in\left(-2\pi;2\pi\right)\) =>\(\frac{k\pi}{2}\in\left(-2\pi;2\pi\right)\) =>\(\frac{k}{2}\in\left(-2;2\right)\) =>k∈(-4;4)=>k∈{-3;-2;-1;0;1;2;3}=>Phương trình có 7 nghiệm thuộc khoảng \(\left(-2\pi;2\pi\right)\) =>Chọn DCâu 5:\(\sin\left(x+\frac{\pi}{4}\right)=1\) =>\(x+\frac{\pi}{4}=\frac{\pi}{2}+k2\pi\) =>\(x=\frac{\pi}{4}+k2\pi\) \(\pi\le x\le5\pi\) =>\(\pi\le\frac{\pi}{4}+k2\pi\le5\pi\) =>\(1\le2k+\frac14\le5\) =>\(\frac34\le2k\le\frac{19}{4}\) =>\(\frac38\le k\le\frac{19}{8}\) mà k nguyênnên k∈{1;2}=>Có 2 nghiệm=>Chọn BCâu 6: cosx=1=>\(x=k2\pi\) =>Chọn ACâu 7: cos2x=-1=>\(2x=\pi+k2\pi\) =>\(x=\frac{\pi}{2}+k\pi\) =>Chọn CCâu 8: \(cos\left(x+\frac{\pi}{6}\right)=0\) =>\(x+\frac{\pi}{6}=\frac{\pi}{2}+k\pi\) =>\(x=\frac{\pi}{3}+k\pi\) =>Chọn DCâu 9: cos2x=1=>\(2x=k2\pi\) =>\(x=k\pi\) \(x\in\left\lbrack-2\pi;4\pi\right\rbrack\) =>\(k\pi\in\left\lbrack-2\pi;4\pi\right\rbrack\) =>k∈[-2;4]=>k∈{-2;-1;0;1;2;3;4}=>Có 7 nghiệm=>Chọn DCâu 10: \(cos\left(x+\frac{5\pi}{4}\right)=-1\) =>\(x+\frac54\pi=\pi+k2\pi\) =>\(x=\frac{-1}{4}\pi+k2\pi\) =>Nghiệm dương nhỏ nhất là: \(x=-\frac14\pi+2\pi=\frac74\pi\) =>Chọn ACâu 11: 2*sin x-1=0=>sin x=1/2=>\(\left[\begin{array}{l}x=\frac{\pi}{6}+k2\pi\\ x=\pi-\frac{\pi}{6}+k2\pi=\frac56\pi+k2\pi\end{array}\right.\) =>Chọn ACâu 12: \(2\cdot cosx+\sqrt2=0\) =>\(2\cdot cosx=-\sqrt2\) =>\(cosx=-\frac{\sqrt2}{2}\) =>\(\left[\begin{array}{l}x=\frac34\pi+k2\pi\\ x=-\frac34\pi+k2\pi\end{array}\right.\) =>Chọn BCâu trả lời: Câu 4: sin 2x=0=>\(2x=k\pi\) =>\(x=\frac{k\pi}{2}\) \(x\in\left(-2\pi;2\pi\right)\) =>\(\frac{k\pi}{2}\in\left(-2\pi;2\pi\right)\) =>\(\frac{k}{2}\in\left(-2;2\right)\) =>k∈(-4;4)=>k∈{-3;-2;-1;0;1;2;3}=>Phương trình có 7 nghiệm thuộc khoảng \(\left(-2\pi;2\pi\right)\) =>Chọn DCâu 5:\(\sin\left(x+\frac{\pi}{4}\right)=1\) =>\(x+\frac{\pi}{4}=\frac{\pi}{2}+k2\pi\) =>\(x=\frac{\pi}{4}+k2\pi\) \(\pi\le x\le5\pi\) =>\(\pi\le\frac{\pi}{4}+k2\pi\le5\pi\) =>\(1\le2k+\frac14\le5\) =>\(\frac34\le2k\le\frac{19}{4}\) =>\(\frac38\le k\le\frac{19}{8}\) mà k nguyênnên k∈{1;2}=>Có 2 nghiệm=>Chọn BCâu 6: cosx=1=>\(x=k2\pi\) =>Chọn ACâu 7: cos2x=-1=>\(2x=\pi+k2\pi\) =>\(x=\frac{\pi}{2}+k\pi\) =>Chọn CCâu 8: \(cos\left(x+\frac{\pi}{6}\right)=0\) =>\(x+\frac{\pi}{6}=\frac{\pi}{2}+k\pi\) =>\(x=\frac{\pi}{3}+k\pi\) =>Chọn DCâu 9: cos2x=1=>\(2x=k2\pi\) =>\(x=k\pi\) \(x\in\left\lbrack-2\pi;4\pi\right\rbrack\) =>\(k\pi\in\left\lbrack-2\pi;4\pi\right\rbrack\) =>k∈[-2;4]=>k∈{-2;-1;0;1;2;3;4}=>Có 7 nghiệm=>Chọn DCâu 10: \(cos\left(x+\frac{5\pi}{4}\right)=-1\) =>\(x+\frac54\pi=\pi+k2\pi\) =>\(x=\frac{-1}{4}\pi+k2\pi\) =>Nghiệm dương nhỏ nhất là: \(x=-\frac14\pi+2\pi=\frac74\pi\) =>Chọn ACâu 11: 2*sin x-1=0=>sin x=1/2=>\(\left[\begin{array}{l}x=\frac{\pi}{6}+k2\pi\\ x=\pi-\frac{\pi}{6}+k2\pi=\frac56\pi+k2\pi\end{array}\right.\) =>Chọn ACâu 12: \(2\cdot cosx+\sqrt2=0\) =>\(2\cdot cosx=-\sqrt2\) =>\(cosx=-\frac{\sqrt2}{2}\) =>\(\left[\begin{array}{l}x=\frac34\pi+k2\pi\\ x=-\frac34\pi+k2\pi\end{array}\right.\) =>Chọn B