中考数学资料三倍角公式推导
<p>三倍角公式推导</p><p>tan3=sin3/cos3</p><p>=(sin2cos+cos2sin)/(cos2cos-sin2sin)</p><p>=(2sincos^2()+cos^2()sin-sin^3())/(cos^3()-cossin^2()-2sin^2()cos)</p><p>上下同除以cos^3()，得：</p><p>tan3=(3tan-tan^3())/(1-3tan^2())</p><p>sin3=sin(2+)=sin2cos+cos2sin</p><p>=2sincos^2()+(1-2sin^2())sin</p><p>=2sin-2sin^3()+sin-2sin^3()=3sin-4sin^3()</p><p>cos3=cos(2+)=cos2cos-sin2sin</p><p>=(2cos^2()-1)cos-2cossin^2()</p><p>=2cos^3()-cos+(2cos-2cos^3())</p><p>=4cos^3()-3cos</p><p>即</p><p>sin3=3sin-4sin^3()</p><p>cos3=4cos^3()-3cos</p>
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