5cos^2a+4cos^2β=4cosα则cos^2a+cos^2β

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/13 11:29:05

5cos^2a+4cos^2β=4cosα
令cosα = t
5t^2+4cos^2β=4t
4cos^2β=4t-5t^2
4cos^2β≥0
4t-5t^2≥0
5t^2-4t≤0
t(5t-4)≤0
0≤t≤4/5
5cos^2a+4cos^2β=4cosα
4cos^2a+4cos^2β=4cosα-cos^2α=4-4+4cosα-cos^2α=4-(2-cosα)^2=4-(2-t)^2
0≤t≤4/5
0≥ -t ≥ -4/5
2 ≥ 2-t ≥ 6/5
4 ≥ (2-t)^2 ≥ 36/25
-4≤-(2-t)^2≤-36/25
0≤4-(2-t)^2≤64/25
即0≤4cos^2a+4cos^2β≤64/25
0≤cos^2a+cos^2β≤16/25

已知5(cosα)^2+4(cosβ)^2=4cosα,则(cosα)^2+(cosβ)^2的取值范围是? 化简(1-sin^6 a-cos^6 a)/(cos^2 a-cos^4 a)== 证明sin(4A)sin(2A)(1-cos(2A)) cos(4A)cos(2A)(1 cos(2A))=cos(2A 化简 1-sin^4a-cos^4a/cos^2a-cos^4a Cos(a+b)*cos(a-b)=1/5 求cos ^2-sin^2 已知4sin asin b=根号2,4cos a cos b=根号6,则cos 2a+cos 2b的值是? 求证:a^2(cos^2b-cos^2c)+b^2(cos^c-cos^2a)+c^2(cos^2a-cos^2b)=0 cos(pai/15)×cos(2pai/15)×cos(3pai/15)×cos(4pai/15)×cos(5pai/ p=cos a/cos 2a怎么化简? 若sin^4a/sin^2b+cos^4a/cos^2b=1,证明sin^4b/sin^2a+cos^4b/cos^2a 向量a=(cosα,sinα),b=(cosβ,sinβ)若|√2 *a+b|=|a-2b|,则cos(α-β)=? 已知向量a=(cosα,sinα),b=(cosβ,sinβ),|a-2b|=|√2a+b|,则cos(α-β)=___