Question

prove that secA(1-sinA) (secA+tanA)=1.​

Answer 1

Step-by-step explanation:

sin^A + cos^A = 1 and therefore cos^2A = 1 - sin^2A

secA =1/cosA

tan A = sinA/cosA

secA(1 - sinA)(secA + tanA) works out to

[(1/cosA)(1 - sinA) (1/cosA+sinA/cosA)]

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

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

(1 - sin^2 A) / cos^2 A --------> for reasons given above

cos^2 A / Cos^2 A

=1