题目内容
已知sin(α-
)=
，α∈[
，
]，则cosα=______．
| π |
| 4 |
| 3 |
| 5 |
| 3π |
| 4 |
| 5π |
| 4 |
∵α∈[
，
]，∴α-
∈[
，π]，∴cos(α-
)=-
，
∴cosα=cos[(α-
)+
]=cos(α-
)cos
-sin(α-
)sin
=-
×
-
×
=-
故答案为：-
．
| 3π |
| 4 |
| 5π |
| 4 |
| π |
| 4 |
| π |
| 2 |
| π |
| 4 |
| 4 |
| 5 |
∴cosα=cos[(α-
| π |
| 4 |
| π |
| 4 |
| π |
| 4 |
| π |
| 4 |
| π |
| 4 |
| π |
| 4 |
=-
| 4 |
| 5 |
| ||
| 2 |
| 3 |
| 5 |
| ||
| 2 |
7
| ||
| 10 |
故答案为：-
7
| ||
| 10 |
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