sin(a+β)cos(r-β)-cos(β+a)sin(β-r)跟tan5π/4+tan5π/12 / 1-tan5π/12要怎么算

题目

sin(a+β)cos(r-β)-cos(β+a)sin(β-r)跟tan5π/4+tan5π/12 / 1-tan5π/12要怎么算

答案

sin(a+β)cos(r-β)-cos(β+a)sin(β-r)=sin(a+β)cos(r-β)-cos(a+β)sin[-(r-β)]=sin(a+β)cos(r-β)+cos(a+β)sin(r-β)=sin[(a+β)+(r-β)]=sin(a+r)[(tan5π/4)+(tan5π/12)]/[1-(tan5π/12)]=[(tan(π+π/4))...