How do I write tan(2 sin^1(x)) as an algebraic expression?
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1 answer

Consider a rightangled triangle with hypotenuse = 1, and opposite = x
sinθ = opposite/hypotenuse = x/1
then by Pythagoras the adjacent side = √(1x^2)
and cosθ = √(1x^2)
sin^1(x) is the angle θ so that sinθ = x
then tan(2 sin^1 (x) )
= tan (2θ)
= sin 2θ / cos 2θ
= 2sinθcosθ/(cos^2 θ  sin^2 θ)
= 2x√(1x^2) / (1x^2  x^2)
= 2x√(1x^2) / (1 2x^2) 👍
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