Exercício sobre trigonometria

(FUVEST - 1998)
a) Expresse $\phantom{X}\operatorname{sen}3\,\alpha\phantom{X}$ em função de $\phantom{X}\operatorname{sen}\alpha\,$.
b) Resolva a inequação $\phantom{X}\operatorname{sen}3\,\alpha\;\gt\;2\operatorname{sen}\alpha\phantom{X}\,$ para $\phantom{X}0\,\lt\,\alpha\,\lt\,\pi\;$.

resposta: a) sen3α = 3.senα - 4.sen³α
b)$\,S\,=\,$ $\lbrace\,\alpha\,\in\,{\rm\,I\!R}\,|\,0\,\lt\,\alpha\,\lt\,\frac{\,\pi\,}{\,6\,}\;{\text ou}\;\frac{\,5\pi\,}{\,6\,}\,\lt\,\alpha\,\lt\,\pi\,\rbrace\,$
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