Question

tan A / 1+ Sec A - tan A/ 1- sec A = 2 cosec A
prove lhs = rhs​

Answer 1

HEY MATE HERE IS YOUR ANSWER ✍✍

➡️tanA/1+secA  -  tanA/1-secA

= (tanA - tanA*secA - tanA - tanA*secA)/(1+secA)(1-secA)

= (-tanA*secA - tanA*secA)/(1-sec2A)

= secA( -tanA - tanA)/ -tan2A                          [Since 1+tan2A = sec2A  or 1-sec2A = -tan2A]

= -2*tanA*secA/ -tan2A

 

Cancelling the negative sign and the "tanA" in the numerator and the denominator, we get,

2*tanA*secA/ tan2A tanA

= 2*secA / tanA

= ( 2*1/cosA) / (sinA/cosA)

Cancelling "1/cosA" in the numerator and the denominator,

( 2*1/cosA) / (sinA/cosA)

= 2/sinA

= 2*cosecA                                 [Since 1/sinA = cosecA]

= R.H.S.

Hence proved.

HOPE YOU GOT YOUR ANSWER ✌