Final answer:
To find the value of tanθ when x = 2sinθ, you can use the Pythagorean identity for trigonometric functions. The expression for tanθ is (2sinθ)/(± √(1 - x^2/4)).
Step-by-step explanation:
To find the value of tanθ when x = 2sinθ, you can use the Pythagorean identity for trigonometric functions. The Pythagorean identity states that sin^2θ + cos^2θ = 1. Since x = 2sinθ, we can square both sides to get x^2 = 4sin^2θ. Rearranging this equation, we have sin^2θ = x^2/4. We can subtract this equation from the Pythagorean identity: 1 - sin^2θ = cos^2θ. Simplifying this equation, we get cos^2θ = 1 - x^2/4. Taking the square root of both sides, we have cosθ = ± √(1 - x^2/4). Finally, since tanθ = sinθ/cosθ, we can substitute the expressions for sinθ and cosθ to get tanθ = (2sinθ)/(± √(1 - x^2/4)).