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If sec θ – tan θ = 1 , the value of sec θ . tan θ is √3
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1 3 -
1 √3 -
4 √3 -
1 √3
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Correct Option: A
| secθ – tanθ = | ....(i) | √3 |
∵ sec²θ – tan²θ = 1
⇒ (secθ + tanθ) (secθ – tanθ) = 1
⇒ secθ + tanθ = 3 ....(ii)
On adding equations (i) and (ii)
| 2secθ = √3 + | √3 |
| = | = | √3 | √3 |
| ⇒ secθ = | √3 |
Again, by equation (ii) – (i),
| 2 tanθ = √3 - | √3 |
| = | = | √3 | √3 |
| ⇒ tanθ = | √3 |
∴ secθ . tanθ
| = | × | = | √3 | √3 | 3 |
