If tan x = x - (1/4x), then sec x - tan x is equal to
a) -2x, 1/2x
b) -1/2x, 2x
c) 2x
d) 2x, 1/2x
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Solution:
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)
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