- #1

Krushnaraj Pandya

Gold Member

- 697

- 73

## Homework Statement

Show that ##\arcsin 2x \sqrt{1-x^2} = 2 \arccos{x}## when 1/√2 < x < 1

## Homework Equations

All trigonometric and inverse trigonometric identities, special usage of double angle identities here

## The Attempt at a Solution

I can get the answer by puting x=cosy, the term inside arcsin becomes 2cosysiny=sin2y, so the answer is 2y=2arccosx

BUT

why can't I put x=siny and obtain the answer as 2arcsinx as in the case when 1/√2< x <1/√2