Sin13°cos3°-sin5°sin85°-cos8°cos82°

Sin13°cos3°-sin5°sin85°-cos8°cos82°=
sin13°cos3°-sin5°cos(90°-85°)-cos8°sin(90°-82°)=
sin13°cos3°-(2sin5°cos5°+2cos8°sin8°)/2=
sin13°cos3°-(sin10°+sin16°)/2=
sin13°cos3°-(sin(13°-3°)+sin(13°+3°))/2=
sin13°cos3°-(sin13°cos3°-cos13°sin3°+sin13°cos3°+cos13°sin3°)/2=
sin13°cos3°-(2sin13°cos3°)/2=
sin13°cos3°-sin13°cos3°=0