1.“sin^2 alpha +sin^2 beta =1”是“sin alpha +cos beta =0”的（）.

[题目]若 sin alpha =dfrac (1)(3), 则 cos 2alpha = ()()-|||-

19.设α，β，γ是向量a的三个方向角，则sin^2alpha+sin^2beta+sin^2gamma=____.19.(填空题，3.0分)设α，β，γ是向量

7.[福建2020适应性模拟]已知 tan alpha =2 ,则-|||-dfrac ({sin )^2alpha -(cos )^2alpha +2}(2{

beta_1 = alpha_1, beta_2 = alpha_1 + alpha_2, beta_3 = alpha_1 + alpha_2 + alpha

设 alpha (alpha )_(1),(alpha )_(2),(alpha )_(3),(beta )_(1),(beta )_(2) 均为四维列向量矩阵

例1(1)(2021·全国甲卷)若 alpha in (0,dfrac (pi )(2)), tan2α-|||-=dfrac (cos alpha )(2-s

已知: alpha_1, alpha_2, alpha_3 线性无关，beta_1 = 2alpha_2 - alpha_3，beta_2 = -alpha_1

6.设α1,α2,α3线性无关, (beta )_(1)=a(alpha )_(1)+b(alpha )_(2) (beta )_(2)=a(alpha )_(

8.若向量组α1,α2,α3线性无关, (beta )_(1)=(alpha )_(1)-(alpha )_(2), (beta )_(2)=(alpha )_

4.设向量组beta_(1)=alpha_(1)+2alpha_(2)-alpha_(3),beta_(2)=alpha_(1)+2alpha_(2)+2alp