[toán 10]lượng giác

D

duyp95

Sin(A+B) + sin(B+C) + cos(C+A)= 3/2
\Leftrightarrow SinC + sinA + cos(C+A)= 3/2
\Leftrightarrow2sin((A+C)/2).cos((A-C)/2) -2(sin((A+C)/2)))^2 -1/2= 0 (1)
Coi (1) la pt bac 2 an sin((A+C)/2) , pt nay co nghiem
\Leftrightarrow Delta \geq 0
\Leftrightarrow (cos((A-C)/2)))^2 \geq 1
ma (cos((A-C)/2)))^2 \leq1
\Rightarrow (1) \Leftrightarrow(cos((A-C)/2)))^2=1;sin((A+C)/2)= cos((A-C)/2) /2 \LeftrightarrowA=C=30 va B=120
Minh trinh bay hoi kem mong ban hieu :D
 
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