If ` 3/2+costheta+isintheta = a+ib `, prove that ` a^2+b^2=4a-3 `

if 3/(2+cos theta+i sin theta)=a+ib then prove that a^2+b^2=4a-3

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

If (ax)/(costheta)+(by)/(sintheta)=a^2-b^2 , and (axsintheta)/(cos^2theta)-(bycostheta)/(sin^2theta)=0 , prove that (ax)^(2/3)+(by)^(2/3)=(a^2-b^2)^(2/3)

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

If a sintheta + bcos theta = C, then prove that a costheta -b sintheta = sqrt(a^2+b^2-c^2)

If cosectheta-sintheta=a^3, sectheta-costheta=b^3 , then prove that a^2b^2(a^2+b^2)=1

If cos e ctheta-sintheta=a^3,sectheta-costheta=b^3, Prove that : a^2b^2(a^2+b^2)=1

If 2costheta-sintheta=x and costheta-3sintheta=ydot Prove that 2x^2+y^2-2x y=5.

If sintheta,costheta be the roots of a x^2+b x+c=0 , then prove that b^2=a^2+2a cdot

If cos e ctheta-sintheta=m and sectheta-costheta=n , prove that (m^(2)n)^(2/3)+(m n^2)^(2/3)=1