Question

tìm tập xác định của hàm số

1.y=\(cot\left(\dfrac{\pi}{3}-x\right)\)

2.y=\(\dfrac{tan2x-1}{\sqrt{1+sinx}+1}\)

3.y=\(\sqrt{\sqrt{1+sinx}-\sqrt{2}}\)

4.y=\(\dfrac{3cos4x-3}{\sqrt{2-2cosx}-2}\)

5.y=\(\dfrac{1-cot3x}{1-\sqrt{1+sin3x}}\)

6.y=\(cot2x+cotx\)

Answer 1

1. \(sin\left(\dfrac{\pi}{3}-x\right)\ne0\Leftrightarrow\dfrac{\pi}{3}-x\ne k\pi\Leftrightarrow x\ne\dfrac{\pi}{3}-k\pi\)

2. \(cos2x\ne0\Leftrightarrow2x\ne\dfrac{\pi}{2}+k\pi\Leftrightarrow x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\)

3. \(\sqrt{1+sinx}-\sqrt{2}\ge0\Leftrightarrow1+sinx\ge2\Leftrightarrow sinx\ge1\Leftrightarrow sinx=1\Leftrightarrow x=\dfrac{\pi}{2}+k2\pi\)

4. \(\sqrt{2-2cosx}-2\ne0\Leftrightarrow2-2cosx\ne4\Leftrightarrow cosx\ne-1\Leftrightarrow x\ne\pi+k2\pi\)

5. \(1-\sqrt{1+sin3x}\ne0\Leftrightarrow sin3x\ne0\Leftrightarrow3x\ne k\pi\Leftrightarrow x\ne\dfrac{k\pi}{3}\)