max and minimum value

thanks aditya.
i did it like this,

i multiplied and divided it by 2 to get,
or, 2(sinx)[sin(x+45)]√2
or, [cos45 - cos(2x+54)]√2
or, [1 - √2 cos(2x+54)]2
now the given function will be minimum at the maximum value of cos(2x+45) that is 1 and maximum at the minimum value of cos(2x+45) that is -1.
so,
1-√22≤ sinx(sinx+cosx)≤1+√22