SOLUTION: For the domain 0<= x < 2pi, how many solutions does the equation 2^sin^2(x) + 2^cos^2(x) = 2 have?

Question 1079574: For the domain 0<= x < 2pi, how many solutions does the equation 2^sin^2(x) + 2^cos^2(x) = 2 have?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

It has no solutions because the least the left side ever gets is
, which is about 2.828, when the left side is p/4, 3p/4, 5p/4, and 7p/4.
The largest it ever gets is 3, when x = 0, p/2, p, and 3p/2.

The left side can never equal 2.  Thus there are no solutions.

Edwin

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