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    Question

    Find the value of sin(θ) if 2sinθ = tanθ, for 0 < θ

    < 90°.
    A 1/2 Correct Answer Incorrect Answer
    B 1/√3 Correct Answer Incorrect Answer
    C √3/2 Correct Answer Incorrect Answer
    D 1 Correct Answer Incorrect Answer

    Solution

    We know that tanθ = sinθ/cosθ. Given 2sinθ = tanθ, we have 2sinθ = sinθ/cosθ. Multiplying both sides by cosθ, we get 2sinθ * cosθ = sinθ. Dividing both sides by sinθ, we get 2cosθ = 1. Thus, cosθ = 1/2. Now, sin²θ = 1 - cos²θ = 1 - (1/2)² = 1 - 1/4 = 3/4, so sinθ = √3/2.

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