`lim_(x to pi//2) (cot x - cos x)/((pi - 2x)^(3))` equalsA. `1/24`B. `1/16`C. `1/8`D. `1/4`

`lim_(x to pi//2) (cot x - cos x)/((pi - 2x)^(3))` equalsA. `1/24`B. `

1.	`lim_(x to pi//2) (cot x - cos x)/((pi - 2x)^(3))` equalsA. `1/24`B. `1/16`C. `1/8`D. `1/4`
Answer» Correct Answer - B `underset ( x to pi//2)lim(cot x - cos x ) /((pi-2x)^(3)) = underset( x to pi//2 ) lim 1/8 * ( cos x ( 1 - sin x ))/(sin x (pi/2 - x )^(3)) ` ` underset ( h to 0) lim 1/8(cos(pi/2 - h)[1 - sin (pi/2 - h)])/(sin(pi/2 - h)(pi/2 - pi/2 + h)^(3))` ` = 1/8 underset ( h to 0 ) lim ( sin h ( 1 - cos h ) )/( cos h h ^(3)) ` ` = 1/8 underset( h to 0 ) lim ( sin h (2 sin ^(2) h/2))/( cos h * h ^(3 )) ` ` = 1/4 underset( h to 0 ) lim ( sin h * sin^(2) ( h/2 ) )/( h ^(3) cos h ) ` ` 1/4 underset ( h to 0 ) lim (( sin h ) /h ) ( ( sin h/2)/( h/2))^(2) * 1/( cos h) * 1/4 = 1/4 xx 1/4 = 1/16`