Prove that `lim_(theta->pi/2) (2cos theta)/(pi-2theta)=1`

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

Given that lim_(theta rarr 0) (sin theta)/theta = 1 and lim_(theta rarr 0) cos theta = 1 Evaluate lim_(theta rarr pi/2) (cot theta)/(pi/2 - theta)

Prove that cos (2theta) /(1+sin 2 theta)=tan(pi/4-theta)

lim _( theta to x //2) ( cos theta )/( ( pi //2-theta))

Evaluate the following limits : Lim_(theta to pi/2)(cot theta)/(pi/2 - theta )

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

Prove that : (cos(pi+theta)cos(-theta))/(sin (pi-theta) cos (pi/2+ theta))= cot^2 theta.

Prove that (cos(pi +theta)cos (-theta))/(cos(pi-theta) cos (pi/2+theta))=-cot theta