Question

tan*/1-cot*+cot*/1-tan*

Answer 1

(tan A)/(1 - cot A) + cot A /(1 - tan A) 

= (tan A)/[(1 - (1/tan A)] + cot A /(1 - tan A) 

= (tan2A)/[(tan A - 1)] + cot A /(1 - tan A) 

= (tan2A)/[(tan A - 1)] - cot A /(tan A - 1) 

= (tan2 A - cot A) / (tan A - 1) 

= (tan2 A - 1/tan A) / (tan A - 1) 

= (tan3 A - 1) / [tan A (tan A - 1)] 

= (tan A - 1)(tan2 A + tan A + 1) / [tan A (tan A - 1)] 

= (tan2 A + tan A + 1) / tan A 

= 1 + tan A + cot A 

= 1 + [(sin A/cosA) + (cos A/sin A)] 

= 1 + [(sin2 A + cos2 A) / sin A cos A] 

= 1 + [1 / (sin A cos A)] = 1 + (sec A x cosA) Hence proved

Answer 2

solve as per your need , or what need to prove ..