3sin^2A +2sin^2B=1,3sin2A- 2sin2B=0,求证A+2B=90度
来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/27 02:46:33
3sin^2A+2sin^2B=1,3sin2A-2sin2B=0,求证A+2B=90度3sin^2A+2sin^2B=1,3sin2A-2sin2B=0,求证A+2B=90度3sin^2A+2sin
3sin^2A +2sin^2B=1,3sin2A- 2sin2B=0,求证A+2B=90度
3sin^2A +2sin^2B=1,3sin2A- 2sin2B=0,求证A+2B=90度
3sin^2A +2sin^2B=1,3sin2A- 2sin2B=0,求证A+2B=90度
因为3(sinA)^2=1-2(sinB)^2=cos2B
3sin2A/2=sin2B
(cos2B)^2+(sin2B)^2=1
所以[3(sinA)^2]^2+(3sin2A/2)^2=1
-->9(sinA)^4+9(sinAcosA)^2=1
-->9(sinA)^4+9(sinA)^2[1-(sinA)^2]=1
设(sinA)^2=t,则9t^2+9t(1-t)=1,
解得t=1/9,从而sinA=1/3,cosA=2*根号2/3.
因为2B∈(0,2π)且cos2B=3(sinA)^2=1/3>0,所以2B∈(0,π).
因为A∈(0,π/2),所以(π/2-A)∈(0,π/2).
由cos2B=sinA=cos(π/2-A)且余弦函数在(0,π/2)有单调性,
可得2B=π/2-A
即A+2B=π/2.证毕.
3 在三角形ABC中,已知(a2+b2)sin(A-B)=(a2-b2)sin(A+B) 求证:ABC是等腰或直角三角形(a^2+b^2)sin(A-B)=(a^2-b^2)sin(A+B),(sin^A+sin^B)sin(A-B)=(sin^A-sin^B)sin(A+B) sin^A*(sin(A+B)-sin(A-B))=sin^B*(sin(A-B)+sin(A+B)) sin^A*2c
3sin(a)^2+2sin(b)^2=1,3sin(a)=2sin(b),a,b都为锐角,求a+2b的值是3sin(2a)=2sin(2b),
已知3SIN^2A+2SIN^2B=5SINA,求SIN^2A+SIN^2B范围
懂得进.证明,sina+sin(a+b)+sin(a+2b)+...sin(a+nb)=sin(a+ab/2)sin[(n+1)b/2]/sin(b/2)
【证明】Sin A+sin B=2Sin 22
sinA=1/2,sinB=1/3,sin(A+B)sin(A-B)=?
sin(a+b)=1/2,sin(a-b)=1/3,则tana/tanb=?
sin(a+b)=1/2,sin(a-b)=1/3,则tana/tanb=?
已知sin(a+b)=1/2,sin(a-b)=1/3,求tana/tanb
已知sin(A+B)=2/3,sin(A-B)=1/5.求tanA/tanB
证明sin(a+b)sin(a-b)=sin^2 a-sin^2 b,
求证:sin(a+b)sin(a-b)=sin^2a-sin^2b
证明 sin^2A+sin^2B-sin^2A*sin^2B+cos^2A*cos^2证明 sin^2A+sin^2B-sin^2A*sin^2B+cos^2A*cos^2B=1
已知sin(a+b)等于2/3,sin(a-b0 =1/5,求tana:tanb
已知 sin a,sin 2x ,cos a 成等差数列,sin a ,sin x ,cos a 成等比数列,求cos 2x 的值.已知 ,3sin^2 a+2sin^2 b=1 ,3sin 2a-2sin 2b=0 且a ,b 为锐角,试求 a+2b的值.
在△ABC中,求证;sin^(A/2)+sin^(B/2)+sin^(C/2)=1-2sin(A/2)sin(B/2)sin(C/2)
已知sin(a)=2sin(b)求sin(a/2)/sin(b/2)的值.
sin阝=1/3,sin(a+阝)=1,求sin(2a+3阝)