Question

Prove that cosA/cosec A+1+cosA/cosecA-1=2 tanA

Answer 1

LHS
[cosA/(cosecA+1)] + [cosA/(cosec-1)]
Taking LCM

=[cosA(cosec-1) + cosA(cosecA+1)]/[(cosecA+1)(cosecA-1)

cosAcosecA = cosA /sinA = cotA

and, (cosecA+1)(cosecA-1)= cosec²A -1 = cot²A

now, substituting these values,
(cotA -cosA)+(cotA +cosA)/cot²A
=2cotA/cot²A
=2/cotA
=2tanA
RHS