Prove that?

Question

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

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Answer 1 · 2018-05-28T16:03:20

I don't think it's true.

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.