1.
a. Đkxđ:
`cosx-1 \ne 0 ⇔ cosx \ne 1 ⇔ x \ne k2π \ (k∈\mathbb{Z})`
Vậy `D=\mathbb{R} \ \setminus \ {k2π, k∈\mathbb{Z}}`
b. Đkxđ:
`sin2x \ne -1 ⇔ 2x \ne -\frac{π}{2}+k2π ⇔ x \ne -\frac{π}{4}+kπ \ (k∈\mathbb{Z})`
Vậy `D=\mathbb{R} \ \backslash \ {-\frac{π}{4}+kπ, k∈\mathbb{Z}}`
c. Đkxđ:
`cos(2x+\frac{π}{3}) \ne 0 ⇔ 2x+\frac{π}{3} \ne \frac{π}{2}+kπ`
⇔ `x \ne \frac{π}{12}+\frac{kπ}{2} \ (k∈\mathbb{Z})`
Vậy `D=\mathbb{R} \ \backslash \ {\frac{π}{12}+\frac{kπ}{2}, k∈\mathbb{Z}}`
d. Đkxđ:
`sin(x-\frac{π}{6}) \ne 0 ⇔ x-\frac{π}{6} \ne kπ`
⇔ `x \ne \frac{π}{6}+kπ \ (k∈\mathbb{Z})`
Vậy `D=\mathbb{R} \ \backslash \ {\frac{π}{6}+kπ, k∈\mathbb{Z}}`
2.
a. `-1≤sinx≤1`
⇔ `2≤sinx+3≤4`
⇔ `2≤y≤4`
b. `-1≤cosx≤1`
⇔ `-3≤3cosx≤3`
⇔ `-7≤3cosx-4≤-1`
⇔ `-7≤y≤-1`
c. `-1≤sinx≤1`
⇔ `2≥-2sinx≥-2`
⇔ `7≥5-2sinx≥3`
⇔ `3≤y≤7`
d. `0≤sin^2x≤1`
⇔ `0≤6sin^2x≤6`
⇔ `-3≤6sin^2x-3≤3`
⇔ `-3≤y≤3`
e. `0≤cos^2x≤1`
⇔ `0≥-5cos^2x≥-5`
⇔ `7≥7-5cos^2x≥2`
⇔ `2≤y≤7`
