` lim _ ( x to pi//2) ( sec x - tan x) ` का मान ज्ञात कीजिये ।

Options

A. `0`
B. `1`
C. `-1`
D. `1/2`

Answer

A

Explanation

` lim _ ( x to pi//2) ( sec x - tan x) = lim _ ( x to pi//2) [ ( 1- sin x)/(cos x)] `
` = lim _ ( x to pi//2) [( (cos ^(2) 1/ x+ sin^(2). 1/2 x) - 2 sin 1/2 x cos 1/2 x]/(cos^(2)1/2 x - sin ^(2). 1/2 x )]`
` = lim _ ( x to pi //2) [(cos1/2x- sin. 1/2 x)^(2)/((cos1/2 x- sin. 1/2 x)( cos1/2 x+ sin 1/2 x))]`
` = lim _( x to pi//2) ((cos1/2x- sin 1/2 x))/((cos1/2 x+ sin 1/2 x))= ( cos. 1/4 pi - sin. 1/4 pi)/( cos. 1/4 pi + sin. 1/4 pi)`
` = ( (1//sqrt(2))- (1//sqrt(2)))/((1//sqrt(2)) + (1//sqrt(2)))= 0/(2//sqrt(2))=0`