Question

How do you prove `2 arcsin x = arccos(1 − 2x^2)`?

Answer 1

Please see below.

Explanation:

Let `sinA=x`, then `arcsinx=A`

Now `cos2A=1-2sin^2A=1-2x^2`

Hence `arccos(1-2x^2)=2A=2arcsinx`