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Question
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
Solution
Consider the table.
| θ | 0° | 30° | 45° | 60° | 90° |
| sin θ | 0 | `1/2` | `1/sqrt2` | `sqrt3/2` | 1 |
| cos θ | 1 | `sqrt3/2` | `1/sqrt2` | `1/2` | 0 |
Here,
`sin 60°-cos 60°=sqrt3/2-1/2>0`
`sin 90°-cos 90°= 1-0>0 `
`so, sin 80°-cos 80° > 0` ` (sin θ-cos θ≥0AA45°≤ θ ≤ 90° )`
Therefore, the given statement is false.
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