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i have to show that in a triangle, there is : (A, B, C are the angles of that triangle)

[tex] \sin \left( 1/2\,B \right) \cos \left( 1/2\,C \right) +\sin \left( 1/2

\,C \right) \cos \left( 1/2\,B \right) =\cos \left( 1/2\,A \right) [/tex]

for this one, here is what i got to...

[tex] 1/4\,\sqrt {2-2\,{\it cosB}}\sqrt {2+2\,{\it cosC}}+1/4\,\sqrt {2-2\,{

\it cosC}}\sqrt {2+2\,{\it cosB}} [/tex]

my question is, i dont have any A in this equation above, and i have to prove that it is equal to cos(a/2)!! i know that cos(a)=cos(pi-(b+c) ... please if someone can help me with that!

for the second one, we have : [tex] \left( \cos \right) \,\alpha={\frac {a}{b+c}} [/tex]

and [tex] \left( \cos \right) \,\beta={\frac {b}{c+a}}

and \left( \cos \right) \,\gamma={\frac {c}{a+b}} [/tex]

and we have to show that:

[tex] 1/2\,{\tan}^{2}\alpha+1/2\,{\tan}^{2}\beta+1/2\,{\tan}^{2}\gamma = 1 [/tex]

this one, i erally dont know what to do! if someone can help me out! or maybe give me hints...

i appreciate your help!!