tan[π4+12cos−1ab]+tan[π4−12cos−1ab]Let cos−1ab=x⇒cosx=abtan[π4+x2]+tan[π4−x2]=tanπ4+tanπ21−tanπ4.tanπ2+tanπ4−tanπ21+tanπ4.tanπ2=1+tanx21−tanx2+1−tanx21+tanx2=(1−tanx2)2+(1−tanx2)2(1−tanx2)(1+tanx2)=2(1+tan2x2)1−tan2x2cos2x=1−tan2x1+tan2xcosx=1−tan2x21+tan2x22×(1+tan2x2)1−tan2x2=2×ba