cos a – sin a + 1/cos a + sin a – 1= cosec a+ cot a

cos a -sin a+1/cos a + sin a -1Dividing by sin a in the numerator and denominatorSo, cos a/sina- sin a/sin a+1/sin a _____________________________ cos a/ sin a+sin a/ sin a-1/sin a So, cot a - 1 +cosec a _________________ cot a + 1- cosec a Then, cosec a + cot a - 1 __________________ 1- cosec a + cot a Then, cosec a + cot a -(cosec^2 a - cot^2) ___________________________________ 1-cosec a + cot a Then, cosec a+cota- {(cosec a+cot a)(cosec a-cot a)}___________________________________________ 1- cosec a + cot a Taking common Then,(cosec a + cot a){ 1 - ( cosec a - cot a)}______________________________________ 1- cosec a + cot aThen, (cosec a + cot a) ( 1- cosec a + cot a)_____________________________________ 1 - cosec a + cot acancelling ( 1- cosec a + cot a) from the numerator and denominator Therefore, LHS=cosec a + cot a=RHS

Approved