`a)A = cos² 20^o + cos² 40^o + cos² 50^o + cos ² 70^o`
`=(cos^2 20^0+cos^2 70^o)+(cos^2 40^o + cos^2 50^o)`
`=(cos^2 20^0+sin^2 20^o)+(cos^2 40^o + sin^2 40^o)`
`=1+1=2`
b)`B= sin^6 alpha + cos^6 alpha + 3sin² alpha - cos² alpha`
`=(sin^alpha)^3+(cos^2alpha)^3+3sin^2alpha+cos^2alpha`
`=(sin^2alpha+cos^2alpha)(sin^4alpha+cos^4alpha+sin^2alphacos^2alpha)+3sin^2alphacos^2alpha`
`=sin^4alpha+cos^4alpha+2sin^2alphacos^2alpha`
`=(sin^2alpha+cos^2alpha)^2=1`