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

Let $\sin A = x$, then $\arcsin x = A$
Now $\cos 2 A = 1 - 2 {\sin}^{2} A = 1 - 2 {x}^{2}$
Hence $\arccos \left(1 - 2 {x}^{2}\right) = 2 A = 2 \arcsin x$