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# Calculate .

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Calculate $$\arccos \sqrt{\cfrac{1+\sqrt{\cfrac{1-\sqrt{\cfrac{1-\sqrt{\cfrac{1+\cfrac{\sqrt{3}}{2}}{2}}}{2}}}{2}}}{2}}$$.

I'm not exactly sure how to approach this, but I have this as progress: $$\arccos \sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}} = \frac{\frac{\pi} {6}} {2}$$. I don't know how to deal with it further, could someone help me?

Mar 20, 2020

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But you have already solved the problem! All you have to do is to take the arccos of the Left Hand Side and that gives you =Pi / 12, which  equals The Right Hand Side of =Pi / 12.

Mar 20, 2020
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LHS =Take the square root of 3 =[1.7320508.... / 2 + 1] / 2 =0.9330127018.....Now take the square root of this: Sqrt(0.9330127018) =0.9659258262890. Then take the arccos of this in radians:arccos(0.9659258262890) =0.26179938779914943653855361527329 = Pi / 12. And that is it !.

Mar 20, 2020