Question

sin²13°＋cos²17°－sin13°cos17°=?

Answer 1

sin²13°+cos17°-sin13°cos17°

=(1-cos26°)/2+(1+cos26°)/2-sin13°cos17°

=1+(cos26°-cos34°)/2-sin13°cos17°

=1-sin[(26°+34°)/2]sin[(26°-34°)/2]-[sin(13°+17°)+sin(13°-17°)]/2

（积化和差公式,和差化积公式）

=1-sin30°sin4°-(sin30°-sin4°)/2

=1-(1/2)sin4°-1/4+(1/2)sin4°

=3/4