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+1 vote
in Mathematics by (1.3k points)
a) -2x, 1/2x

b) -1/2x, 2x

c) 2x

d) 2x, 1/2x

1 Answer

+1 vote
by (9.9k points)
Best answer


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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