Question

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

Answer 1

heya it's Aastha...

◆Taking LHS...

Sec A = x + 1/4x
Tan A = √[(Sec2 A) - 1]
         = √[(x + 1/4x)2 - 1]
         = √[(x2 + 1/16x2 + 1/2) - 1]
         = √[x2 + 1/16x2 - 1/2]
         = √[(x - 1/4x)2]
         = (x - 1/4x)

Sec A + Tan A = (x + 1/4x) + (x - 1/4x)
                      = 2x
LHS =RHS
hence proved...

Answer 2

yes this is the right answer