If tanθ + cotθ = 5, then ta$n^2$θ + co$t^2$θ equals:

Square the given equation: ta$n^2$θ + co$t^2$θ + 2·tanθ·cotθ = 25. Since tanθ·cotθ = 1, this is ta$n^2$θ + co$t^2$θ + 2 = 25, so the value is 23. Squaring without subtracting the cross term gives 25.