QQuestion
If 5 sin² θ + 4 cos² θ = 9\over2, then from this relation find the value of tan θ.
✓Answer
5 sin² θ + 4 cos² θ = 9\over2
⇒ 2(5 sin² θ + 4 cos² θ) = 9
⇒ 10 sin² θ + 8 cos² θ = 9
⇒ 10 sin² θ + 8 (1 – sin² θ) = 9
⇒ 10 sin² θ + 8 – 8sin² θ = 9
⇒ 2 sin² θ = 9 – 8
⇒ sin² θ = 1\over 2
⇒ sin θ = 1\over √2
⇒ sin θ = sin 45° ⇒ θ = 45°
∴ tan θ = tan 45° = 1
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