IIT JEE , AIEEE Forum - Mathematics , Algebra

shailesh_45

prove this one ,

_{[ x}_]

_{[ 0]} ( xtanx)/( 1- cos x) = 2

madman

multiplying and dividing by 1 + cos x we have
lim x (1+cos x)/sin x cos x
lim 2x (1+cosx)/ sin 2x
lim (1+cos x)/ lim sin 2x /2x = lim (1+cos x)/1 = 2

panks_01

_{[x ]}

_{[ 0]} (x tan x) / (1 - cos x)

put 1 - cos x = 2 sin²(x/2)

_{[ x]}

_{[ 0]} (x tan x) / 2 sin²(x/2)

nw divide n multiply numerator by x n denom by x²/4

since x tends to 0

_{[ x]}

_{[ 0]} (x tan x) / 2 sin(x/2) sin(x/2) = x²/x²/2 = 2

since lim tanx/x = 1 and lim sinx/x = 1(wen x tends to 0)

plz rate if corr..........