If 3sin2θ + 5cos2θ= 4 and θ is an acute angle, then the value of tanθ is:
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 1.
3sin2θ + 5cos2θ= 4
⇒ 3sin2θ + 3cos2θ + 2cos2θ = 4
⇒ 3(sin2θ + cos2θ) + 2cos2θ = 4
⇒ 3(1) + 2cos2θ = 4 [∵ sin2θ + cos2θ = 1]
⇒ 3 + 2cos2θ = 4
⇒ 2cos2θ = 4 - 3 = 1
⇒ cos2θ = 1/2
⇒ cosθ = √(1/2) = 1/√2 = cos 45°
⇒ θ = 45°
⇒ tanθ = tan 45° = 1
Therefore, the value of tanθ is 1.