Grade 12Trigonometry
if A+B+C=pi and (5+4cosA)(5-4cosB) = 9 and (13-12cosB)(13-12cosC) = 25 then cos(A+B)+cos(B+C)+cos(C+A) = ??
if A+B+C=pi and (5+4cosA)(5-4cosB) = 9 and (13-12cosB)(13-12cosC) = 25 then cos(A+B)+cos(B+C)+cos(C+A) = ??
1 Answer
Alankriti Mittal
We need to find -(cosA+cosB+cosC)
25-20 cosB+20 cosA-16 cosAcosB=9
20 cosA+16=20cosB+16 cosAcosB
5cosA+4=5 cosB+4
169-156 cosC -156cosB+144 cosBcosC=25
-156(cosC+cosB)=-144 (1+cosBcosC)
13(cosB+cosC)=12(1+cosBcosC)
Now,solve using cosA= - cos(B+C)
You'll get 2 equations having cos B and CosC only...
N will eventually will b able to solve the question
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