# If 7 sin²θ +3cos²θ=4, then the value of tan θ is (θ is acute) :

**Second option is correct
**

**Explanation:-**

7 sin²θ + 3 cos²θ = 4

4 sin²θ + 3 sin²θ + 3 cos²θ = 4

4 sin²θ + 3 (sin²θ + cos²θ) = 4

4 sin²θ + 3 = 4

4 sin²θ = 4 – 3

4 sin²θ = 1

sin²θ = 1/4

Square root on both side,

sinθ = 1/2

sinθ = sin 30°

θ = 30°

Then, the value of tan 30° = 1/√3

Hence, the answer is (2) 1/√3