BITSAT 2015 Paper

Let us assume the functions f(x) and g(x) given by
f(x) = tanx – x and g(x) = x – sinx, for
0 < x <

π

2

Now , f ' (x) = sec2x - 1 and
g ' (x) = 1 - cos x
r f ' (x) > 0 and g ' (x) > 0 for all x ∊ (0,

π

2

)
⇒ f (x) > f (0) and g (x) > g (0) for all x ∊ (0,

π

2

)
⇒ tan x - x > 0 and x - sin x > 0 for all x ∊ (0,

π

2

)
⇒ tan x > x and x > sin x for all x ∊ (0,

π

2

)
⇒ sin x < x < tan x for all x ∊ (0,

π

2

)