## no.identity05 one year ago how to derive cosine law from sine law? can anybody help me.. please..

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1. 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 $$K$$

2. anonymous

now consider $$A+B+C=\pi$$ so expand: $$\sin(\pi-B-C)=\dots\\\sin(\pi-A-C)=\dots\\\sin(\pi-A-B)$$

3. 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

4. Loser66

https://en.wikipedia.org/wiki/Law_of_cosines Read the part "using law of sin", it is exactly what @oldrin.bataku wrote

5. no.identity05

thanks mate..