Question

tanA/secA -1 = tan A+sec A +1 /tan A + sec A -1​

Answer 1

(tanA+secA-1)/(tanA-secA+1)=(1+sinA)/cos A

multiply LHS by cosA /cosA to get  

(sinA+1-cosA) / (sinA-1+cosA)  

multiply again by cosA/cosA to get  

(sinA.cosA+cosA-cos^2A) / cosA(sinA-1+cosA)  

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

= ( cosA(1+sinA) - (1+sinA)(1-sinA) ) / cosA(sinA-1+cosA)  

= ( (1+sinA)(cosA-1+sinA) ) / cosA(sinA-1+cosA)  

= (1+sinA)/cosA