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Calc tg a/2 astfel incat sin a egal cu 3/5

Răspuns :

tg x/2=t

[tex]\it sinx = \dfrac{2t}{1+t^2} \Rightarrow \dfrac{3}{5} = \dfrac{2t}{1+t^2}\Rightarrow 3+3t^2 = 10t \Rightarrow 3t^2-10t+3=0[/tex]

[tex]\it t_{1,2} = \dfrac{5\pm\sqrt{25-9}}{3} =\dfrac{5\pm4}{3} \\\;\\ \\\;\\ \it t_1 = \dfrac{1}{3},\ \ \ t_2 = 3[/tex]