Answer to Question #31896 in Trigonometry for aashish

Question

If tan A + sec A =L , then prove that (L2+L)/2L = sec A
(* note L2 is L square)

Answer 1

This equality (L2+L)/2L=sec(A) is incorrect.
Prove:
(L2+L)/2L=L/2+1/2=sec (A). So, we obtain that L+1=2sec(A) or tan(A)+sec(A)+1=2sec(A). From this
tan(A)+1=sec(A) - but it's wrong equality, because tan^2(A)+1=sec^2(A).