One particular problem asked to solve for the sin(195deg). So, I first attempted with the sum formula, splitting the 195 into 150 and 45. This yielded the result:

. . . . .[tex]\dfrac{\sqrt{2\,}\, -\, \sqrt{6\,}}{4}[/tex]

However, I then wondered what the result would be utilizing the half-

angle formula. Using this, I found the answer to be:

. . . . .[tex]\dfrac{-2\, \sqrt{2\, -\, \sqrt{3\,}\,}}{4}[/tex]

I then set these answers equal to each other and found that -2sqrt(2-sqrt(3)) = sqrt(2) - sqrt(6). Therefore, is there a formula involving nested radicals (like the one found in the half-angle result) that says, for example, what sqrt(A - sqrt(B)) is equivalent to?

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