一道数学题,拜托大家帮一下忙吧

预备知识:
以下这个数字阵横行观察,行数表达的是n的取值,数字表示的是(a+b)^n展开式中按a的降幂排列后各个项的系数.

..............1...1..............n=1
............1...2...1............n=2
..........1...3...3...1..........n=3
........1...4...6...4...1........n=4
......1...5..10..10...5...1......n=5
.....1...6..15..15..15...6...1....n=6
...................................n

所以,
(a+b)^2=a^2+2ab+b^2
(a+b)^3=a^3+3a^2b+3ab^2+b^3
(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4
(a+b)^5=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5
即有:
a^2+b^2=(a+b)^2-2ab
a^3+b^3=(a+b)^3-3a^2b-3ab^2
a^4+b^4=(a+b)^4-4a^3b-6a^2b^2-4ab^3
a^5+b^5=(a+b)^5-5a^4b-10a^3b^2-10a^2b^3-5ab^4

其他理论根据:
sin^2(θ) + cos^2(θ) =1
2sinθcosθ=sin2θ
为了书写方便,
设
sin^2(θ)=A
cos^2(θ)=B
sin^2(2θ)=C
则有
A+B=1
AB=(1/4)*C
A^2+B^2=(A+B)^2-2AB=1-(1/2)*C
u6
=A^3+B^3
=(A+B)^3-3A^2B-3AB^2
1-3