, , ale in G.P. 157. If in a triangle ABC, A = a2 - (b - c)2, then tanA is equal to

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( begin{aligned} Delta &=a^{2}-(b-c)^{2} &=(a-b+c)(a+b-c) text { Now, } & s=frac{a+b+c}{2} Rightarrow & quad s-b=frac{a+b+c-b}{2}=frac{2}{2}=frac{a+b-c}{2} end{aligned} ) ( Rightarrow quad Delta=(a-b+c)(a+b-c)=2(s-b) cdot 2(s-c) ) ( Rightarrow quad Delta=4(s-b)(s-c) ) ( Rightarrow quad sqrt{s(s-a)(s-b)(s-c)}=4(s-b)(s-c) quad ) [lleron's ( Rightarrow quad sqrt{S(s-a)}=4 sqrt{(-b)(s-c)} ) ( Rightarrow quad sqrt{frac{(-b)(s-c)}{s(s-a)}}=frac{1}{4} ) ( Rightarrow tan frac{A}{2}=frac{1}{4} ) ( Rightarrow quad tan A=frac{2 tan gamma / 2}{1-tan ^{2} frac{A}{2}}=frac{2 / 4}{1-frac{1}{16}}=frac{8}{15} ) ( Rightarrow quad tan A=frac{8}{15} quad int frac{operatorname{Phin}(2)}{1} )

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