Question

cotA/1-tanA +tanA/1-cot​ prove this solution

Answer 1

Answer:

tan A / 1- cotA  + cotA/1- tanA = 1 + secAsinA  

LHS  

tanA / 1- cotA  +  cotA / 1- tanA

= tan^2A / tanA - 1  +  1/ tanA(1 - tanA)

= tan ^2A / tanA-1  -  1 / tanA(tanA-1 )  

= tan^3A -1/ tanA(tanA - 1)  

=( tanA-1 )( tan^2A + 1 + tanA ) / tanA ( tanA - 1)

= sec^2 + tanA/tanA

= sec^ 2A / tanA + 1  

=1  + secAcosecA