Question

запишите выражение в виде произведения 3-4cos²a

Answer 1

$\displaystyle\bf\\3-4Cos^{2} \alpha =3-4\cdot\frac{1+Cos2\alpha }{2} =3-2\cdot(1+Cos2\alpha )=\\\\\\=3-2-2Cos2\alpha =1-2Cos2\alpha =1-2\cdot(1-2Sin^{2} \alpha )=\\\\\\=1-2+4Sin^{2} \alpha=4Sin^{2} \alpha -1=(2Sin\alpha )^{2} -1^{2} =\\\\\\=(2Sin\alpha -1)\cdot(2Sin\alpha +1)$