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Câu 2: `cos(x+\frac{\pi}{4})=1`

`\Rightarrow cos(x+\frac{\pi}{4})=cos0`

`\Rightarrow x+\frac{\pi}{4}=k2\pi`

`\Rightarrow x=-\frac{\pi}{4}+k2\pi`

Với `\pi \leq x \leq 5\pi`:

`\Rightarrow \pi \leq -\frac{\pi}{4}+k2\pi \leq 5\pi`

`\Rightarrow \frac{5\pi}{4} \leq k2\pi \leq \frac{21\pi}{4}`

`\Rightarrow \frac{5}{8} \leq k \leq \frac{21}{8}` 

Vậy `0,625 \leq k \leq 2,625` với `k\in \mathbb{Z}`

`\Rightarrow` k=1; k=2

Vậy có 2 nghiệm thuộc `[\pi;5\pi]`

`\Rightarrow` D. 2.

Câu 3: `cosx=0`

`\Rightarrow cos x=cos\frac{\pi}{2}`

`\Rightarrow x=\frac{\pi}{2}+k\pi`

Với `0 < x \leq 2021\pi`

`\Rightarrow 0<\frac{\pi}{2}+k\pi \leq 2021\pi`

`\Rightarrow -\frac{1}{2} < k \leq \frac{4041}{2}`

`\Rightarrow -0,5 < k \leq 2020,5`

Vậy `-0,5 < k \leq 2020,5` với `k\in \mathbb{Z}`

Vậy có 2020 giá trị k thỏa mãn

`\Rightarrow` D. 2020.