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If secθ + tanθ = m (>1), then the value of sinθ is
(0° < θ < 90°)
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1 - m2 1 + m2
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m2 - 1 m2 + 1
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m2 + 1 m2 - 1
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1 + m2 1 - m2
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Correct Option: B
secθ + tanθ = m (Given) ...(i)
∵ sec2θ – tan2θ = 1
⇒ (secθ + tanθ) (secθ – tanθ) = 1
| ⇒ secθ – tanθ = | ....(ii) | |
| m |
By equations (i) + (ii),
| 2secθ = m + | ||
| m |
| ⇒ secθ = | ||
| 2m |
By equation (i) – (ii),
| 2tanθ = m - | ||
| m |
| ⇒ tanθ = | ||
| 2m |
| ∴ sinθ = | ||
| secθ |
| sinθ = | × | = | |||
| 2m | m2 + 1 | m2 + 1 |
