Question

sin57sin102-sin12sin33

Answer 1

$sin57^circ cdot sin102^circ -sin12^circ cdot sin33^circ =\\=sin57^circ cdot sin(90^circ +12^circ )-sin12^circ cdot sin(90^circ -57^circ )=\\=sin57^circ cdot cos12^circ -sin12^circ cdot cos57^circ =\\=sin(57^circ -12^circ )=sin45^circ = frac{sqrt2}{2}$