[toán] lượng giác

D

duyanhkt

theo đẳng thức cơ bản :sinA+sinB+sinC=4cos(A/2)cos(B/2)cos(C/2)=>cos(A/2)cos(B/2)cos(C/2)=(sinA+sinB+sinC)/4(1)
cosA+cosB+cosC=1+4sin(A/2)sin(B/2)sin(C/2)=>sin(A/2)sin(B/2)sin(C/2)=(cosA+cosB+cosC-1)/4(2)
thay (1),(2) vào đề ta có:
sinA+sinB+sinC=1+cosA+cosB+cosC
<=>2sin(A/2)cos(A/2)+2cos(A/2)cos((B-C)/2)=2cos^2(A/2)+2sin(A/2)cos((B-C)/2)
<=>sin(A/2)(cos(A/2)-cos(B-C)/2)=cos(A/2)(cos(A/2)-cos(B-C)/2)
<=>sin(A/2)=cos(A/2)=>A=90' or cos(A/2)=cos(B-C)/2=>B or C = 90'
 
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