Question

Prove the following identities:
TanA+Cot2A=Cosec2A

Answer 1

let us the left hand side of question.
LHS= cot 2A + tan A
as we know-
cot 2A = cos 2A/sin 2A and
tan A = sinA/cosA therefore,
LHS= (cos2A ×cosA + sin2A × sinA)/(sin2A × cosA)
cross multiplication , we know formula's
cos(2A - A) = cos2A × cos A+ sin2A × sinA
So,
LHS = cos(2A -A) / (sin2A × cosA)
LHS = cosA / ( sin2A × cosA)
LHS = 1 / sin2A
LHS = cosec2A
LHS = RHS
therefore,
cot2A + tanA = cosec2A
Hence proved ....