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平面三角中三倍角公式是 sin3α=3sinα-4sin~3α。 cos3α=4cos~3α-3cosα。三倍角公式应用较广,它可以解决一些证明、求值、三角方程、应用题等问题。三倍角公式可以变化成如下形式: sin3α=4sinαsin(60°-α)sin(60°+α) 〈S〉 cos3α=4cosαcos(60°-α)cos(60°+α) 〈C〉 tg3α=tgα·tg(60°-α)tg(60°+α) 〈T〉证明:sin3α=3sin-4sin~3α=4sinα(3/4-sin~2α)=4sinα(sin60°-sina)(sin60°+sinα)=4sinαsin(60°-α)sin(60°+α)。
The triple angle formula in the plane triangle is sin3α=3sinα-4sin~3α. Cos3α=4cos~3α-3cosα. The triple angle formula is widely used, it can solve some problems such as proof, evaluation, trigonometric equations and application problems. The triple angle formula can be changed to the following form: sin3α=4sinαsin(60°-α)sin(60°+α) 〈S〉 cos3α=4cosαcos(60°-α)cos(60°+α) 〈C〉 tg3α=tgα ·tg(60°-α)tg(60°+α) Proof: sin3α=3sin-4sin~3α=4sinα(3/4-sin~2α)=4sinα(sin60°-sina)(sin60°+ Sinα = 4sinαsin(60°-α)sin(60°+α).