Prove that `lim_(theta to 0)(sintheta)/(theta)=1"("theta` measured in radians)

Statement 1 lim_(xtopi//2)(sin(cot^(2)x))/((pi-2x)^(2))=1/2 Statement 2: lim_(theta to 0)(sin theta)/(theta)=1 and lim_(theta to 0)(tan theta)/(theta)=1 , where theta is measured in radians.

lim_(theta rarr3^(+))([theta])/(theta)

Prove that- 1-cos^2theta/(1+sintheta)=sintheta

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

Using L'Hospital 's rule prove that lim_(theta rarr 0) (theta-sintheta)/(theta^3)=1/6

lim_(theta rarr0)cot theta-csc theta

lim_(theta rarr0)((sin theta)/(sin((theta)/(2))))=2

lim_(theta rarr0)(1-cos theta)/(sin^(2)2 theta)

Prove that sqrt((1+sintheta)/(1-sin theta))=sectheta+tantheta .

Prove that:- (cos(theta/2)+sin(theta/2))^2=1+sintheta