Using `("lim")_(thetavec0)(sintheta)/theta-1` prove that the area of circle of radius `R` is `piR^2` (Figure)

By using intergration prove that the area of a circle of radius r units is pir^2 square units.

Area of a circle = 2pir^(2) .

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

The area of a sector of angle theta^(@) of a circle with radius R is

Prove that sintheta/(1-costheta)=cosectheta+cot theta

If r sintheta=3,r=4(1+sintheta),0lethetale2pi,"then "theta=

If sintheta + costheta = sqrt(3) , then prove that tantheta + cot theta =1 .

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.

Prove that: sqrt((1-sintheta)/(1+sintheta))=sectheta -tan theta .