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In a right-angled triangle XYZ, right-angled at Y, if XY = 2 √6 and XZ – YZ = 2, then sec X + tan X is
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- 1 √6 - √6
- 2√6
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- √6 2
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Correct Option: B
XZ – YZ = 2 .... (i)
⇒ XY² + YZ² = XZ²
⇒ ⇒ (2√6)² XZ² - YZ²
⇒ 24 = (XZ – YZ) (XZ + YZ)
⇒ XZ +YZ = 12 ....(ii)
Adding both the equations,
2 X Z = 14 ⇒ XZ = 7
∴ YZ = 7 – 2 = 5
| ∴ sec X = | 2√6 |
| & tan X = | 2√6 |
| ∴ sec X + tanX = | + | 2√6 | 2√6 |
| = | = √6 | 2√6 |
