find the minimum value of the expression

1/(cos²(pi/4+x)+sin²(pi/4-x))

we can write cos^2(pi/4+x)= cos^2(pi/2-(pi/4-x)= sin^2(pi/4-x)
1/(2sin^2(pi/4-x)
the value will be minimum when sin^2(pi/4-x) will be maximum that is
sin^2(pi/4-x)=1
so the minimum value is ½ [ans]