Question

Преобразуйте в произведение выражение:
даю 30баллов​

Answer 1

$\displaystyle\bf\\1)\\\\Sin^{2} \alpha -Sin^{2} \beta =(Sin\alpha -Sin\beta )(Sin\alpha +Sin\beta )=\\\\\\=2Sin\frac{\alpha -\beta }{2} Cos\frac{\alpha +\beta }{2} \cdot2Sin\frac{\alpha +\beta }{2} Cos\frac{\alpha -\beta }{2} =\\\\\\=4Sin\frac{\alpha -\beta }{2} Cos\frac{\alpha +\beta }{2} Sin\frac{\alpha +\beta }{2} Cos\frac{\alpha -\beta }{2}$

$\displaystyle\bf\\2)\\\\\frac{3}{4} -Sin^{2}x=\Big(\frac{\sqrt{3} }{2} \Big)^{2} -Sin^{2} x=Sin^{2}60^\circ-Sin^{2}x=\\\\\\=2Sin\frac{60^\circ -x }{2} Cos\frac{60^\circ +x }{2} \cdot2Sin\frac{60^\circ +x }{2} Cos\frac{60^\circ -x }{2} =\\\\\\=4Sin\frac{60^\circ -x }{2} Cos\frac{60^\circ +x }{2}Sin\frac{60^\circ +x }{2} Cos\frac{60^\circ -x }{2}$