几道数学简单的2倍角函数题(1)tana-1/tana=-2/tan2a(2)tan(a+pai/4)+tan(a-pai/4)=2tan2a(3)1+sin2a/sina+cosa=sina+cosa(4)sina(1+cos2a)=sin2acosa(5)2sin(pai/4+a)sin(pai/4-a)=cos2a(6)1+sin2a-cos2a/1+sin2a+cos2a=tana
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![几道数学简单的2倍角函数题(1)tana-1/tana=-2/tan2a(2)tan(a+pai/4)+tan(a-pai/4)=2tan2a(3)1+sin2a/sina+cosa=sina+cosa(4)sina(1+cos2a)=sin2acosa(5)2sin(pai/4+a)sin(pai/4-a)=cos2a(6)1+sin2a-cos2a/1+sin2a+cos2a=tana](/uploads/image/z/7837299-27-9.jpg?t=%E5%87%A0%E9%81%93%E6%95%B0%E5%AD%A6%E7%AE%80%E5%8D%95%E7%9A%842%E5%80%8D%E8%A7%92%E5%87%BD%E6%95%B0%E9%A2%98%281%29tana-1%2Ftana%3D-2%2Ftan2a%282%29tan%28a%2Bpai%2F4%29%2Btan%28a-pai%2F4%29%3D2tan2a%283%291%2Bsin2a%2Fsina%2Bcosa%3Dsina%2Bcosa%284%29sina%281%2Bcos2a%29%3Dsin2acosa%285%292sin%28pai%2F4%2Ba%29sin%28pai%2F4-a%29%3Dcos2a%286%291%2Bsin2a-cos2a%2F1%2Bsin2a%2Bcos2a%3Dtana)
几道数学简单的2倍角函数题(1)tana-1/tana=-2/tan2a(2)tan(a+pai/4)+tan(a-pai/4)=2tan2a(3)1+sin2a/sina+cosa=sina+cosa(4)sina(1+cos2a)=sin2acosa(5)2sin(pai/4+a)sin(pai/4-a)=cos2a(6)1+sin2a-cos2a/1+sin2a+cos2a=tana
几道数学简单的2倍角函数题
(1)tana-1/tana=-2/tan2a
(2)tan(a+pai/4)+tan(a-pai/4)=2tan2a
(3)1+sin2a/sina+cosa=sina+cosa
(4)sina(1+cos2a)=sin2acosa
(5)2sin(pai/4+a)sin(pai/4-a)=cos2a
(6)1+sin2a-cos2a/1+sin2a+cos2a=tana
几道数学简单的2倍角函数题(1)tana-1/tana=-2/tan2a(2)tan(a+pai/4)+tan(a-pai/4)=2tan2a(3)1+sin2a/sina+cosa=sina+cosa(4)sina(1+cos2a)=sin2acosa(5)2sin(pai/4+a)sin(pai/4-a)=cos2a(6)1+sin2a-cos2a/1+sin2a+cos2a=tana
(1)∵左边=(tan²a-1)/tana
=-2(1-tan²a)/(2tana)
=-2/(2tana/(1-tan²a))
=2/tan2a (∵tan2a=2tana/(1-tan²a))
=右边
∴原命题成立;
(2)∵左边=(tana+tan(π/4))/(1-tanatan(π/4))+(tana-tan(π/4))/(1+tanatan(π/4))
=(tana+1)/(1-tana)+(tana-1)/(1+tana)
=((tana+1)²-(tana-1)²)/(1-tan²a)
=4tana/(1-tan²a)
=2tan2a (∵tan2a=2tana/(1-tan²a))
=右边
∴原命题成立;
(3)∵左边=(sin²a+cos²a+2sinacosa)/(sina+cosa)
=(sina+cosa)²/(sina+cosa)
=sina+cosa
=右边
∴原命题成立;
(4)∵左边=sina*2cos²a
=(2sinacosa)cosa
=sin2acosa
=右边
∴原命题成立;
(5)∵左边=cos((pai/4+a)-(pai/4-a))-cos((pai/4+a)+(pai/4-a))
=cos2a-cos(pai/2)
=cos2a
=右边
∴原命题成立;
(6)∵左边=(sin²a+cos²a+2sinacosa-cos²a+sin²a)/(sin²a+cos²a+2sinacosa+cos²a-sin²a)
=(2sin²a+2sinacosa)/(2cos²a+2sinacosa)
=2sina(sina+cosa)/(2cosa(sina+cosa))
=sina/cosa
=tana
=右边
∴原命题成立.