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If sec θ + tan θ = 2 + √5 , then the value of sin θ + cos θ is :
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3 √5
- √5
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7 √5 -
1 √5
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Correct Option: A
sec θ + tan θ = 2 + √3
| ∴ sin θ - tan θ = | √5 + 2 |
[∵ sec² θ - tan² θ = 1]
| = | = √5 - 2 | (√5 + 2)(√5 - 2) |
On adding,
2secθ = 2 + √5 + √5 - 2 = 2√5
| ⇒ secθ = √5 ⇒ cosθ = | √5 |
On subtracting,
2tanθ= 2 + √5 - √5 + 2 = 4
⇒ tan θ = 2
| ∴ | = sin θ | sec θ | √5 |
| ∴ sin θ + cos θ | + | √5 | √5 |
| = | √5 |
