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The Tangent Law

From Sine Law,     
    →b = 2R sin B............(i)
    →c = 2R sin C............(ii)
Subtracting eqn (ii) from (i)        
    b - c = 2R(sin B - sin C)............(I)
Adding eqn (i) and (ii) 
    b + = 2R(sin B + sin C)............(II)
Dividing eqn (I) and (II) 

This verifies the Tangent Law, the remaining result follow similar process.