Simplify \tan(\sin^{-1}(x))

Roger Smith 2021-12-16 Answered
Simplify tan(sin1(x))
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Expert Answer

Ben Owens
Answered 2021-12-17 Author has 27 answers
Let sin1(x)=θ, then x=sinθ
If we draw a right triangle with hypotenuse equal to 1 and the other side equals to x.
From pythagorean theorem: 1x2 is the other side.
Thus, tanθ=sinθcosθ=sinθ1sin2θ
As x=sinθ
Now, we have:
tanθ=x1x2
From sin1(x)=θ we get
tan(sin1(x))=x1x2

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Terry Ray
Answered 2021-12-18 Author has 50 answers
tan(arcsin(x))=x1x21x2

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