Question

Prove that:
$\frac{tana}{1-cota}$=$\frac{cota}{1-tana}$=1+tana+cota

Answer 1

hello dear,

(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)

= (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

I HOPE ITS HELP YOU DEAR, :-)