The maximum value of `cos^2(45^0+x)+(sinx-cosx)^2` is ______

Answer

3

Explanation

`cos ^(2) (45^(@)+ x) + ( sin x - cos x)^(2)`
`" " = [ (cosx )/(sqrt2) - ( sin x)/(sqrt2)]^(2) + (sinx - cos x )^(2)`
`= (3)/(2) ( 1- sin 2 x)`
Hence, Maximum value = `(3)/(2) (1-(-1)) = 3`