If sinθ − cosθ = 1/2, then si$n^4$θ + co$s^4$θ equals:

Squaring gives 1 − 2sinθ·cosθ = 1/4, so sinθ·cosθ = 3/8. Then si$n^4$θ + co$s^4$θ = $1-2(3/8{)}^2=1-9/32=23/32$. Forgetting to square the product (using $1-2p$ with $p=1/16$) or flipping the sign produces the other choices.