Question

prove that (tanA+tanA/2)+1=secA

Answer 1

1+ tan(A)·tan = tan(A)cot - 1 = sec(A) We will make use of the half angle identities: tan = , and its reciprocal cot = , also tan(A) = and sec(A) = First we will prove: 1 + tan(A)·tan = sec(A) 1 +  1 +  Get an LCD  +  Combine fractions over the LCD  Cancel first and third terms on top:   Cancel the sines:   sec(A)