Question

how to derive cosine law from sine law? can anybody help me.. please..

Answer 1

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 \(K\)

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

thanks mate..