Question

If secA + tanA = 2a and secA – tanA = b then the value of ab is

(A) 1 

(B) -1 

(C) 1/2

(D) 1/4

Answer 1

Correct option is (C) 1/2

\(\sec A + \tan A = 2a\)  ....(i)

\(\sec A – \tan A = b\)  ....(ii)

Multiplying by eq (i) to eq (ii),

\((\sec A + \tan A) (\sec A - \tan A) = 2a \times b \)

\(\sec^2 A - \tan^2 A = 2ab\)

\(1 = 2ab\)

\(\therefore ab = \frac 12\)