Question

SecA(1-SinA)*(SecA+tanA)=1.Prove

Answer 1

secA=1/cosA
secA(1-sinA)=1/cosA(1-sinA)=1/cosA-sinA/cosA=secA-tanA
WE HAVE AN IDENTITY THAT sec^2A-tan^2A=1
therefore SecA(1-SinA)*(SecA+tanA)=sec^2A-tan^2A=1

Answer 2

SecA(1-sin A)*(secA+tanA)=1
 LHS;
Converting everything to sinA and cosA;

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

Solving;
=>{ ( 1-sinA ) / cosA }{ (1+sinA)/cosA) }

Multiplying both the brackets

=>(1-sin²A)/cos²A

Since Sin²A+cos²A=1
so, cos²A=1-sin²A

=> cos²A/cos²A
=1 

hence, LHS= RHS

Thus Proved,