If sin⁡xa=cos⁡xb=tan⁡xc=k then bc+1ck+ak1+bk is equal to

bc+1ck+ak1+bk=cos⁡xtan⁡xk2+1tan⁡x+sin⁡x1+cos⁡x=sin⁡xk2+cos⁡x(1+cos⁡x)+sin2⁡xsin⁡x(1+cos⁡x)=ak+cos⁡x(1+cos⁡x)+1−cos2⁡xsin⁡x(1+cos⁡x)=ak+1sin⁡x=ak+1ak