Question

prove that tan A/(1- cot A) + cot A/(1- tan A) = sec A. cosec A+ 1​

Answer 1

Answer:

RHS=LHS

Step-by-step explanation:

ttan A/(1-cotA)+ CotA/(1−tanA)=1+secAcscA

Taking L.H.S.-

tanA/(1−cotA)+CotA/(1−tanA)= tanA/1−(1/tanA)+(1/tanA)/1-tanA

=Tan^2A/tanA-1 + 1/tanA(1−tanA)

=1-tan^3A/tanA/(1−tanA)

=(1-tanA)(1+tanA+tan^2A)/tanA(1−tanA)

=sec^2+tanA/tanA. (∵1+tan=sec^2A)

=1+Sec^2/TanA

=1+1/cosAsinA

=1+secA cosecA

=RHS