求值:(1).(1+cot75°)/(1-cot75°) (2).sin70°sin65°-sin20°sin25°(3).tan(α+5π)=1/2,则(cosα-1/2sinα)/(cosα+sinα) 求详解
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![求值:(1).(1+cot75°)/(1-cot75°) (2).sin70°sin65°-sin20°sin25°(3).tan(α+5π)=1/2,则(cosα-1/2sinα)/(cosα+sinα) 求详解](/uploads/image/z/5187686-14-6.jpg?t=%E6%B1%82%E5%80%BC%3A%281%29.%281%2Bcot75%C2%B0%29%2F%281-cot75%C2%B0%29+%282%29.sin70%C2%B0sin65%C2%B0-sin20%C2%B0sin25%C2%B0%283%29.tan%28%CE%B1%2B5%CF%80%29%3D1%2F2%2C%E5%88%99%28cos%CE%B1-1%2F2sin%CE%B1%29%2F%28cos%CE%B1%2Bsin%CE%B1%29+%E6%B1%82%E8%AF%A6%E8%A7%A3)
求值:(1).(1+cot75°)/(1-cot75°) (2).sin70°sin65°-sin20°sin25°(3).tan(α+5π)=1/2,则(cosα-1/2sinα)/(cosα+sinα) 求详解
求值:(1).(1+cot75°)/(1-cot75°) (2).sin70°sin65°-sin20°sin25°
(3).tan(α+5π)=1/2,则(cosα-1/2sinα)/(cosα+sinα) 求详解
求值:(1).(1+cot75°)/(1-cot75°) (2).sin70°sin65°-sin20°sin25°(3).tan(α+5π)=1/2,则(cosα-1/2sinα)/(cosα+sinα) 求详解
(1+cot75°)/(1-cot75°)
=(1+1/tan75°)/(1-1/tan75°)
=[(tan75°+1)/tan75°]/[(tan75°-1)/tan75°]
=(tan75°+1)/(tan75°-1)
=-(tan75°+1)/(1-tan75°)
=-(tan75°+tan45°)/(1-tan75°tan45°)
=-tan(75°+45°)
=-tan120°
=-tan(180°-60°)
=tan60°
=√3
sin70°sin65°-sin20°sin25°
=sin70°sin(90°-25°)-sin(90°-70°)sin25°
=sin70°cos25°-cos70°sin25°
=sin(70°-25°)
=sin45°
=√2/2
tan(α+5π)=1/2,
tan(α+4π+π)=1/2,
tan(α+π)=1/2,
tanα=1/2,
(cosα-1/2sinα)/(cosα+sinα) 分子分母同时除以cosα
=(cosα/cosα-1/2sinα/cosα)/(cosα/cosα+sinα/cosα)
=(1-1/2tanα)/(1+tanα)
=(1-1/2*1/2)/(1+1/2)
=(1-1/4)/(3/2)
=(3/4)/(3/2)
=3/4*2/3
=1/2