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

If x = 3 sin theta + 4 cos theta and y = 3 cos theta - 4 sin theta then prove that x^(2) + y^(2) = 25 .

if (3)/(2+cos theta+i sin theta)=a+ib then (a-2)^(2)+b^(2) equals to:

If x = 3sin theta + 4cos theta and y = 3cos theta - 4 sin theta then prove that x^(2) + y^(2) = 25 .

If a sin^(3) theta + b cos^(3) theta = sin^(3) theta * cos theta and a sin theta - b cos theta=0 , then prove that a^(2)+b^(2)=1 .

If (3)/(2+cos theta+i sin theta)=a+ib and a^(2)+b^(2)=a lambda-3, then the value of lambda, is

If "cosec" theta - sin theta = a^(3) and sec theta - cos theta = b^(3) , then prove that a^(2)b^(2)(a^(2) + b^(2))= 1.

If sin(pi cos theta)=cos(pi sin theta) ,then prove that : theta=(1)/(2)sin^(-1)(3/4)

If x = sin theta + cos theta sin 2 theta " and " y = cos theta + sin theta sin 2 theta,"prove that " (x+y)^(2//3) + (x-y)^(2//3) = 2

If cos ec theta-sin theta=a^(3),sec theta-cos theta=b^(3) then prove that a^(2)b^(2)(a^(2)+b^(2))=1

If cos ec theta-sin theta=a^(3),sec theta-cos theta=b^(3) then prove that a^(2)b^(2)(a^(2)+b^(2))=1