1选B
sin(π-α)=sinα
cos(2π-α)=cos(-α)=cosα
tan(-α+3/2*π)=tan(-α+1/2*π)=ctgα= cosα/ sinα
cos(-π-α)=cos(π+α)=-cosα
f(α)=sinα*cosα*( cosα/ sinα)/ -cosα=-cosα
f(-31π/3)= -cos(-31π/3)= -cos(31π/3)=- -cos(π/3+10π)= -cos(π/3)=-1/2
2选D
A+B+C=π
A+B=π-C
(A+B)/2=π/2-C/2
cos(A+B)=cos(π-C)=-cosC
sin(A+B)=sin(π-C)=sinC
tan(A+C)=tan(π-B)=tan(-B)=-tanB
sin(B+C)/2=sin(π/2-A/2)=cos(A/2))
3 原式=91/2
过程
cos90°=sin0° (cos0°)^2+( cos90°)^2=(cos0°)^2+ (sin0°)^2=1
同理第二项+倒数第二项=1
一共91项高中数学必刷题三角函数视频讲解，一共45组，中间项是(cos45°)^2=1/2
原式=45+1/2=91/2
4
cos(20°-α)=cos(90°-(70°+α))= sin(70°+α)
-180°<α<-90°
-110°<70°+α<-20°
sin(70°+α)<0
因为Cos(70°+α)=1/3
所以sin(70°+α)=- √（1-（1/3）^2=-2/3√3
cos(20°-α)= -2/3√3