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If tan 15° = 2 – √3 , the value of tan 15° cot 75° + tan 75° cot 15°is
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- 14
- 12
- 10
- 8
Correct Option: A
tan 15° . cot 75° + tan 75°. cot 15°
= tan 15°. cot (90° – 15°) + tan (90° – 15°). cot 15°
= tan² 15° + cot2 15° ......(i)
tan 15° = 2 - √3
∴ cot 15°
| = | = | 2 - √3 | (2 - √3)(2 + √3) |
= 2 + √3
∴ tan² 15° + cot² 15°
= (2 - √3)² + (2 + √3)²
= 2 (4 + 3) = 14
