Тригонометрия. Упростите выражение (sina/tga)^2+(cosa/tga)^2-2sin^2a

[latex](\frac{sin\alpha}{tg\alpha})^{2}+(\frac{cos\alpha}{ctg\alpha})^{2}-2sin^{2}\alpha=(sin\alpha\cdot\frac{cos\alpha}{sin\alpha})^{2}+(cos\alpha\cdot\frac{sin\alpha}{cos\alpha})^{2}\\-2sin^{2}\alpha=cos^{2}\alpha+sin^{2}\alpha-2sin^{2}\alpha=1-2sin^{2}\alpha=cos2\alpha[/latex]