If `x+iy=(3)/(2+costheta+isintheta),` prove that :
`" "(x-1)(x-3)+y^(2)=0`.

If x+iy=3/(2+costheta +i sin theta) , then show that x^2+y^2=4x-3

If x=(1+sintheta)/(costheta) , prove that : sintheta=(x^(2)-1)/(x^(2)+1)

Express 1/(1-costheta+2isintheta) in the form x+i y .

If x=a(1-costheta) , y=a(theta+sintheta) , prove that (d^2y)/(dx^2)=-1/a at theta=pi/2 .

If x=a(1+costheta) , y=a(theta+sintheta) , prove that (d^2y)/(dx^2)=(-1)/a at theta=pi/2 .

If x=costheta , y=s in^3theta , prove that y\ (d^2y)/(dx^2)+((dy)/(dx))^2=3\ s in^2theta(5\ cos^2theta-1) .

If (3)/(2+costheta+isintheta)=a+ib" where "i=sqrt(-1) and a^(2)+b^(2)=lamdaa-3," the value of " lamda is

If x=a(theta+sintheta) , y=a(1+costheta) , prove that (d^2y)/(dx^2)=-a/(y^2) .

If x=(2sintheta)/(1+costheta+sintheta) , then prove that (1-costheta+sintheta)/(1+sintheta) is equal to x .

If cottheta+tantheta=x and sectheta-costheta=y , prove that (x^2y)^(2/3)-(x y^2)^(2/3)=1