Question

Simplify tan(sin^−1 x)

Answer 1

make a triangle

Answer 2

it is just for a reference
that is a picture of a triangle with an angle whose sine is \(x\)\you need the other side of the triangle, which you find by memory or pythagoaras
it is
\[\sqrt{1-x^2}\]

Answer 3

tangent is opposite over adjacent

Answer 4

i.e.
\[\tan(\sin^{-1}(x))=\frac{x}{\sqrt{1-x^2}}\]

Answer 5

hope it is more or less clear
this gimmick works for all problems like
\[\sin(\cos^{-1}(x))\] etc

Answer 6

Thank You!