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If sin A = 3 and cos B = 12 , what is the value of tanA - tanB 5 13 1 + tanA tanB
; it being given that A and B are acute angles?
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15 63 -
19 63 -
17 65 -
16 63
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Correct Option: D
| sin A = | |
| 5 |
∴ cos A = √1 - sin²A
| = √ 1 - | |
| 25 |
| = √ | = √ | = | |||
| 25 | 25 | 5 |
| cos B = | |
| 13 |
sin B = √1 - cos²B
| = √ 1 - | |
| 169 |
| = √ |  | 1 - |  | ² | |
| 13 |
| = √ 1 - | = √ | = √ | = | ||||
| 169 | 169 | 169 | 5 |
| ∴ tanA = | = | |||
| sinA | = | |||
| cosA | 4 | |||
| 5 |
| ∴ tanB = | = | |||
| sinB | = | |||
| cosB | 12 | |||
| 13 |
| ∴ | - | |||||
| tanB - tanB | = | 4 | 12 | |||
| 1 + tanA.tanB | 1 + | . | ||||
| 4 | 12 | |||||
| = | |
| 12 | |
| 1 + | |
| 16 | |
| = | |
| 3 | |
| 16 | |
| = | × | = | |||
| 3 | 21 | 63 |
