If 7 sin²θ + 3 cos²θ = 4, (0°

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If 7 sin²θ + 3 cos²θ = 4, (0° < θ < 90°), then the value of tan θ is

1. 1
  √3
2. 1
  2
3. 1
4. √3

Correct Option: A

7 sin²θ + 3cos²θ = 4
On dividing both sides by cos²θ 7 tan²θ + 3 = 4 sec²θ
⇒ 7 tan²θ + 3 = 4 (1+ tan²θ)
⇒ 7 tan²θ + 3 = 4 + 4 tan²θ
⇒ 7 tan²θ – 4 tan²θ = 4 – 3
⇒ 3 tan²θ = 1

⇒ tan²θ =	1
	3

⇒ tanθ =	1
	√3