Hello Sir,
Range of 2sin(ex-1+½π-x) is in [-2,2] since it is a sine function.
Range of πx²-1+π1-x² is (0,inf] since it is sum of exponential function.
On taking 1st derivative of RHS we get:
-2 π^(1 - x^2) xlog(π) + 2 π^(-1 + x^2) xlog(π)
So the critical numbers are:
0,1,-1
Putting the value of 0,1 and -1 in RHS we get π + 1/π, 2 and 2 respectively.
So the minimum value of RHS is 2.
Since Maximum of LHS is 2 and Minimum of RHS is 2,
Edit:
And it happens when x= -1 or x = 1
But @x =-1 LHS is less than 2,
So the correct answer is x = 1