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The value of q, which satisfies the equation tan²θ + 3 = 3 secθ, 0° ≤ θ < 90° is
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- 15° or 0°
- 30° or 0°
- 45° or 0°
- 60° or 0°
Correct Option: D
tan²θ + 3 = 3 sec θ
⇒ sec²θ – 1 + 3 = 3 sec θ
⇒ sec²θ – 3 sec θ + 2 = 0
⇒ sec²θ – 2 sec θ – sec θ + 2 = 0
⇒ secθ (sec θ – 2) – 1 (sec θ – 2) = 0
⇒ (sec θ – 2) (sec θ – 1) = 0
⇒ secθ = 2 or 1
⇒ θ = 60° or 0°.
