化简sin^2(a)sin^2(b)+cos^2(a)cos^2(b)-1/2cos2a*cos2b

来源：学生作业帮助网编辑：作业帮时间：2024/05/06 04:32:15

化简sin^2(a)*sin^2(b)+cos^2(a)*cos^2(b)-1/2cos2a*cos2b
化简sin^2(a)*sin^2(b)+cos^2(a)*cos^2(b)-1/2cos2a*cos2b

化简sin^2(a)*sin^2(b)+cos^2(a)*cos^2(b)-1/2cos2a*cos2b
利用公式把变量的形式化简得越少越好
(sina)^2*(sinb)^2+(cosa)^2*(cosb)^2-1/2cos2a*cos2b
=(1-(cosa)^2)(1-(cosb)^2)+(cosa)^2*(cosb)^2-1/2(2(cosa)^2-1)(2(cosb)^2-1)
=1+(cosacosb)^2-(cosa)^2-(cosb)^2+(cosacosb)^2-1/2[1-2(cosa)^2-2(cosb)^2+4(cosacosb)^2]
=1+2(cosacosb)^2-(cosa)^2-(cosb)^2-1/2+(cosa)^2+(cosb)^2-2(cosacosb)^2
=1-1/2
=1/2

sin^2(a)*sin^2(b)+cos^2(a)*cos^2(b)-1/2cos2a*cos2b
=sin^2(a)*sin^2(b)+cos^2(a)*cos^2(b)-1/2(cos^2(a)-sin^2(a))(cos^2(b)-sin^2(b))
=1/2(sin^2(a)*sin^2(b)+cos^2(a)*cos^2(b)+cos^2(a)*sin^2(b)+sin^2(a)*cos^2(b))
=1/2(sin^2(a)*(sin^2(b)+cos^2(b))+1/2(cos^2(a)*(cos^2(b)+sin^2(b))
=1/2+sin^2(a)+1/2cos^2(a)
=1/2

化简（sin(a-b)-2sin a cos b）/2sin a sin b +coa(a+b) 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【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 sin^2(-a)化简懂得进.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) 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 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）化简cos(a+b)cos(a-b)+sin^2b 化简：sin^2a+sin^2b+2sina*sinb*cos(a+b) sin∧2a+sin∧2b+2sina*sinb*cos(a+b).化简, 化简sin^2a+sin^2b+2sinasinbcos（a+b）