1）tan(5π/12)=tan(π/4+π/6)=[tan(π/4)+tan(π/6)]/[1-tan(π/4)tan(π/6)]
=(1+√3/3)/(1-√3/3)=2+√3 ；
sin165°=sin(120°+45°)=sin120°cos45°+cos120°sin45°=√3/2*√2/2-1/2*√2/2=(√6-√2)/4,
所以 tan(5π/12)/sin165°=4(2+√3)/(√6-√2)=1+√3 .
2）cos20°cos(a-20°)-cos70°sin(a-20°)
=sin70°cos(a-20°)-cos70°sin(a-20°)
=sin[70-(a-20°)]=sin(90°-a)=cosa ；
3）因为 (sinθ)^2+sinθ=1 ,(sinθ)^2+(cosθ)^2=1 ,
所以 sinθ=(cosθ)^2 ,
因此 (cosθ)^2+(cosθ)^4=sinθ+(sinθ)^2=1 .