Prove that?

arcsin(x)^3 + arccos(x)^3 = alpha x has no roots for alpha<1/32 and alpha>7/8

1 Answer
May 28, 2018

I don't think it's true.

Explanation:

See this example, in which I plot arcsin^3(x)+arccos^3(x) and 10x.

According to your claim, they should have no intersection, since alpha=10>7/8, but as you can see, they have.