Question

prove that
tan o/1-cot o + cot o/1-tan o = 1+sec o cosec o
(hint : write the expression in terms of sin o cos o
​

Answer 1

Step-by-step explanation:

tan A)/(1 - cot A) + cot A /(1 - tan A) = (tan A)/[(1 - (1/tan A)] + cot A /(1 - tan A) = (tan2 A)/[(tan A - 1)] + cot A /(1 - tan A) = (tan2 A)/[(tan A - 1)] - cot A /(tan A - 1) = (tan2 A - cot A) / (tan A - 1) = (tan2A - 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 cos A) Hence proved