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The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin-1(sinx), -pie<=x<=pie, is:

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1+cos2x= 2cos2x;  

using this and putting it in given expression I will get cosx = sin-1sinx.   ,-π <= x <= π  

Now  draw the curves of cosx  for  -π <= x <= π  and also draw the curve of sin-1sinx for -π <= x <= π and find the no. of intersection points of the curve. They will intersect at two points only. 

So, Ans is 2.

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