Question
Find the value of sin(θ) if 2sinθ = tanθ, for 0 < θ
< 90°.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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