Question

if sec alpha =x +1/4x : rove that sec alpha =2x or 1/2x

Answer 1

SecA = x+1/4x [given]

since , sec2A - tan2A =1 [ take A = alpha ]


         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

HOPE THIS WOULD HELP YOU OUT