If sec A = x + 1/4x then prove that tan A + secA = 2x or 1/2x

SecA = x+1/4x [given]

since , sec²A - tan²A =1

         sec²A -1 = tan²A

          [x +1/ 4x]² -1 = tan²A

           x2 + 1/16x2 -1/2 = tan²A

tan A = x - 1/4x   or   - [ x-1/4x]

so now , tanA + secA = x - 1/4x + x + 1/4x = 2x

if tanA = -[x-1/4x]

then tanA +secA = -x + 1/4x +x + 1/4x  = 1/2x

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