Question

Prove that
(sec A-1)/(secA+1)=(1-cosA)/(1+cosA)​

Answer 1

$\rm{(sec A-1)/(secA+1)=(1-cosA)/(1+cosA)} \\ \\ \leadsto \bf{ \frac{sec A-1}{secA+1} } = \frac{1 - cosA}{1+cosA}$

Solving the LHS,

$\to \tt \dfrac{ \frac{1}{cosA} - 1 }{ \frac{1}{cosA} + 1 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bigg\{ secA = \frac{1}{cosA} \bigg\}\\ \\ \to \tt \dfrac{ \frac{1 - cosA}{cosA} }{ \frac{1 + cosA}{cosA}} \\ \\ \rm {}{cosA} \: \: gets \: \: cancelled. \\ \\ \to \red{\sf \frac{1 - cosA}{1 + cosA} }$

Thus, RHS has been obtained on solving the LHS.

Hence,

$\sf \huge \red{LHS = RHS}$