If tan2 θ – 3sec θ + 3 = 0, 0°<θ<90°, then the value of sin θ + cos θ is:
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Correct answer: A
Explanation
The correct answer is option 1 i.e. (√3+1)/2.
tan2θ – 3secθ + 3 = 0
Since it is given, (0° ≤ θ ≤ 90°)
Putting θ = 60°
⇒ tan260°– 3sec60° + 3 = 0
⇒ 3 – 2 × 3 + 3 = 0
⇒ 3 – 6 + 3 = 0
⇒ 0 = 0 (Satisfied)
⇒ sinθ + cotθ
⇒ sin60° + cos60°
⇒ (√3/2) + (1/2)
⇒ (√3+1)/2