Cot a-1+cosec a/cot a +1-cosec a= (cot a+cosec a)-1/cot a-cosec a+1=cot a +cosec a- (cosec^2a-cot^2a)/cot a - cosec a+1=(cot a+cosec a)-(cot a+cosec a)(cosec a-cot a)/cot a-cosec a+1=(cot a+cosec a)[1-(cosec a-cot a)]/cot a-cosec a+1=(cot a+cosec a)(1+cot a-cosec a)/cot a- cosec a+1=cot a +cosec a=(cos a/sin a)+1/sin a=1+cos a/sin a