no.identity05
  • no.identity05
how to derive cosine law from sine law? can anybody help me.. please..
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
the law of sines tells us that for a triangle with sides \(a,b,c\) and opposite angles \(A,B,C\) we have $$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}c=K$$ for some constant \(K\)
anonymous
  • anonymous
now consider \(A+B+C=\pi\) so expand: $$\sin(\pi-B-C)=\dots\\\sin(\pi-A-C)=\dots\\\sin(\pi-A-B)$$
no.identity05
  • no.identity05
i really don't get your point, can you show me how? this formulas must be use (a/sinA)=(b/sinB)=(c/sinC)=2R where R is raduis of circumcircle and area of triangle=(1/2)(ab)sinC

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Loser66
  • Loser66
https://en.wikipedia.org/wiki/Law_of_cosines Read the part "using law of sin", it is exactly what @oldrin.bataku wrote
no.identity05
  • no.identity05
thanks mate..

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