If tan x = x - (1/4x), then sec x - tan x is equal to

Question

a) -2x, 1/2x

b) -1/2x, 2x

c) 2x

d) 2x, 1/2x

Answer 1

We know that sec²x-tan²x = 1

sec²x = 1+tan²x

sec²x = 1 + {x - (1/4x)}²

sec²x = 1 + x² + 1/16x² - 2*x*1/4x

sec²x = 1 + x² + 1/16x² - 1/2

sec²x = (x+1/4x)²

sec x = +- (x+1/4x)

So, sec x - tan x = x+1/4x - x+1/4x,  or -x-1/4x - x +1/4x

sec x - tan x = 1/2x,  or -2x

so, correct option is (A)