sin(2arcsin(x))=2x*sqrt(1-x^2)

[Karma]

how is this proof derived?

[dynamicsolo]

how is this proof derived?

Start by defining an angle \theta , so that sin \theta = x . Make a picture of a right triangle illustrating this. Also, replace arcsin(x) by \theta on the left side of your equation: what do you get and what is that equal to? How could you describing that result in terms of the triangle you drew?

[Karma]

Thanks for the explanation .. I understand know.