Question

prove that (tan theta + sec theta -1)/(tan theta - sec theta +1) =(1+sin theta)/cos theta​

Answer 1

Step-by-step explanation:

Let, theta=A

tanA+secA-1/tanA-secA+1=1+sinA/cosA

L.H.S.— tanA+secA-1/tanA-secA+1

=(tanA+secA)-(sec²A-tan²A)/tanA-secA+1

[1=sec²A-tan²A]

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

=(tanA+secA){1-(secA-tanA)}/tanA-secA+1

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

=tanA+secA

=sinA/cosA+1/cosA

=sinA+1/cosA

=R.H.S.