Помогите упростить выражения

1) cos(π/3-α)+cos(π/3+α)=cosπ/3cosα+sinπ/3sinα+cosπ/3cosα-sinπ/3sinα=0.5cosα+0.5cosα=cosα
2)(sin(π+α)+cos(π/2+α))²+(cos(2π-α)-sin(3π/2-α))²=(-sinα-sinα)²+(cosα+cosα)²=4sin²α+4cos²α=4(sin²α+cos²α)=4
3) $\frac{1+cos2 \alpha }{1-cos2 \alpha } = \frac{sin^{2} \alpha + cos^{2} \alpha + cos^{2} \alpha - sin^{2} \alpha }{ sin^{2} \alpha + cos^{2} \alpha - cos^{2} \alpha + sin^{2} \alpha } = \frac{ 2cos^{2} \alpha }{ 2sin^{2} \alpha }= ctg^{2} \alpha$