`lim_(theta to (pi)/(2)) ((pi)/(2)-theta)/(cot theta)` is equal to

lim_(theta rarr pi/2) (pi/2- theta)/(cot theta) =

cot((3 pi)/(2)-theta)+cot[2 pi+theta]=

Evaluate the following limits : Lim_(theta to pi/2) (1-sin theta)/((pi/2-theta)cos theta)

lim_(x rarr(pi)/(2))(1-sin theta)/(((pi)/(2)-theta)cos theta)=

lim_(theta rarr(pi)/(2))(sec theta-tan theta)/(pi-2 theta)

Putting x = theta- (pi) / (4) prove that lim_ (theta rarr (pi) / (4)) (sin theta-cos theta) / (theta- (pi) / (4)) = sqrt (2)

sin((pi)/(2)+theta)+sin((3 pi)/(2)+theta)+sin((5 pi)/(2)+theta)+sin((7 pi)/(2)+theta) is equal to

Evaluate the limits : Lim_(theta to pi/6) (cot^(2) theta - 3)/(" cosec " theta - 2)