sin^2a+sin^2b-sin^2a * sin^2b+cos^2a * cos^2b 化简

来源：学生作业帮助网编辑：作业帮时间：2024/04/28 16:41:27

sin^2a+sin^2b-sin^2a * sin^2b+cos^2a * cos^2b 化简
sin^2a+sin^2b-sin^2a * sin^2b+cos^2a * cos^2b 化简

sin^2a+sin^2b-sin^2a * sin^2b+cos^2a * cos^2b 化简
结果是1
(sina)^2+(sinb)^2-(sina)^2*(sinb)^2+(cosa)^2*(cosb)^2
=(sina)^2*(1-sinb^2)+(sinb)^2+(cosa)^2*(cosb)^2
=sina^2*cosb^2+cosa^2*cosb^2+sinb^2
=(sina^2+cosa^2)*cosb^2+sinb^2
=cosb^2+sinb^2
=1

1
sin^2a(1-sin^2b)+sin^2b+cos^2acos^b
=sin^2a*cos^2b+sin^2b+cos^2acos^2b
=cos^2b*(sin^2a+cos^2a)+sin^2b
=cos^2b+sin^2b
=1

sin^2a+sin^2b-sin^2a * sin^2b+cos^2a * cos^2b
=sin^2a-sin^2a * sin^2b+cos^2a * cos^2b+sin^2b
=sin^2a(1- sin^2b)+cos^2a * cos^2b+sin^2b
=sin^2a cos^2b+cos^2a * cos^2b+sin^2b
= cos^2b(sin^2a +cos^2a )+sin^2b
=cos^2b+sin^2b
=1

原式=sin^2a(1-sin^2b)+sin^2b+cos^2a*(1-sin^2b)=(1-sin^2b)(sin^2a+cos^2a)+sin^2b=cos^2b+sin^2b=1

1+1=2

=sin^2(a)*(1-sin^2(b))+sin^2(b)+cos^2(a)*cos^2(b)
=(sin^2(a)+cons^2(a))*cos^2(b)+sin^2(b)
=cos^2(a)+sin^2(b)
=1

【证明】Sin A+sin B=2Sin 22 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 已知sin(a)=2sin(b)求sin(a/2)/sin(b/2)的值. 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 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sina sin(a+2b) - sinb sin(b+2a) =sin(a+b)sin(a-b) 化简（sin(a-b)-2sin a cos b）/2sin a sin b +coa(a+b) 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 化简sin^2a+sin^2b-sin^2a*sin^2b+cos^2a*cos^2b sin^2a+sin^2b-sin^2a * sin^2b+cos^2a * cos^2b 化简 sin^2 (A)+sin^2(B)-sin^2(A)sin^2(B)+cos^2(A)cos^2(B) 在△ABC中,求证；sin^(A/2)+sin^(B/2)+sin^(C/2)=1-2sin(A/2)sin(B/2)sin(C/2） sin(arccos(2sin(a)))= 设A,B为锐角,且sin^2A+sin^B=sin(A+B),求证A+B＝90sin^2A+sin^2B=sin(A+B)sin^2A表示sinA的平方已知3SIN^2A+2SIN^2B=5SINA,求SIN^2A+SIN^2B范围 sin^2 A=sin^2 B+sinBsinC+sin^2 C 求A角若sin^2a