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If secθ + tanθ = √2, find the value of sinθ.
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1 2
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1 4
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1 √2
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1 3
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Correct Option: D
secθ + tanθ = √2 ....(i)
∵ sec²θ – tan²θ = 1
⇒ (secθ + tanθ) (secθ – tanθ)= 1
⇒ secθ – tanθ = 1/√2 ....(ii)
On adding (i) and (ii),
| 2secθ = √2 + | ||
| √2 |
| ⇒ secθ = | ||
| 2√2 |
On subtracting equation (ii) from (i),
| 2tanθ = √2 - | = | ||
| √2 | √2 |
| ⇒ tanθ = | ||
| 2√2 |
| ∴ sinθ = | = | |||
| tanθ | = | |||
| secθ | 3 | |||
| 2√2 |
