sin(a)+sin(b)=(√2)/2 求cos(a)+cos(b)的范围sin(a)+sin(b)=(√2)/2 求cos(a)+cos(b)的范围
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sin(a)+sin(b)=(√2)/2求cos(a)+cos(b)的范围sin(a)+sin(b)=(√2)/2求cos(a)+cos(b)的范围sin(a)+sin(b)=(√2)/2求cos(a
sin(a)+sin(b)=(√2)/2 求cos(a)+cos(b)的范围sin(a)+sin(b)=(√2)/2 求cos(a)+cos(b)的范围
sin(a)+sin(b)=(√2)/2 求cos(a)+cos(b)的范围
sin(a)+sin(b)=(√2)/2 求cos(a)+cos(b)的范围
sin(a)+sin(b)=(√2)/2 求cos(a)+cos(b)的范围sin(a)+sin(b)=(√2)/2 求cos(a)+cos(b)的范围
设cosA+cosB=k,
∵(sinA+sinB)^2+(cosA+cosB)^2=2+2cos(A-B)
∴1/2+k^2=2+2cos(A-B)
∴cos(A-B)=(k^2-3/2)/2
∵-1≤cos(A-B)≤1
∴-1≤(k^2-3/2)/2≤1
∴-√14/2≤k≤√14/2
即cosA+cosB的范围是:[-14/2 ,√14/2]
【证明】Sin A+sin B=2Sin 22
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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
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在三角形ABC中,若(a^2+b^2)sin(A-B)=(a^2-b^2)sin(A+B),则三角形是?a/sinA=b/sinB=k则a=ksinA,b=ksinB代入(a^2+b^2)sin(A-B)=(a^2-b^2)sinC并把k约分(sin²A+sin²B)sin(A-B)=(sin²A-sin²B)sin(A+B) sin²A*[sin(A+B)-sin(A-B)