( A) सिद्ध कीजिये कि ( A) ` lim _( x to 0) (1- cos x)/x =0`

Explanation

` lim _( x to 0) ( 1- cos x)/x = lim_( x to 0) ( 2 sin^(2). (x/2))/x`
` = lim _( x to 0) [1/2((sin. x/2)/(x/2))^(2).x]`
` = 1/2 lim_( x to0) [((sin. (x/2))/(x/2))]lim x _( x to0)`
` = 1/2 (1)^(2) .0 = 0 " "` इति सिद्धम ।