求值:(1).(1+cot75°)/(1-cot75°) (2).sin70°sin65°-sin20°sin25°
问题描述：
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
答
(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