Question

prove that cotA + Tan A=cosecA. secA​

Answer 1

Step-by-step explanation:

cotA=1/tan A

now,

LHS = 1/tanA+tanA

1+ tan^2/tanA

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

1/cos^2A/ sinA/cosA

(sec^A =1/cos^2A) and ( tan A= sinA /cos A)

1/cosA/sinA

cosecA. secA

(1/cosA= secA ,and1/sinA =cosecA)

LHS =RHS

Answer 2

Step-by-step explanation:

L.H.S= cot A + tan A

cos A/sin A + sin A/ cos A

by doing L.C.M, we get

(cos^2A  + sin^2A )/ sinA cosA

1 / sinA cosA                          (using sin^2A + cos^2A = 1)

1/sinA*1/cosA

cosecA secA                           (1/sinA = cosecA and 1/cosA = secA)

R.H.S = cosecA secA

.: L.H.S=R.H.S

.: cotA + tanA = cosecA secA

HOPE THIS WAS HELPFUL