If `cos^(-1)(x/a)+cos^(-1)(y/b)=theta` ,then the value of `sqrt((x^(2))/(a^(2))+(y^(2))/(b^(2))-(2xy)/(ab)cos theta)` is equal to

If cos ^(-1) .(x)/(a)+ cos ^(-1). (y)/(b) = theta then prove that (x^(2))/(a^(2)) -(2xy)/(ab) . cos theta+ (y^(2))/(b^(2)) = sin ^(2) theta .

If cos^(-1)(x)/(2)+cos^(-1)(y)/(3)=theta then the maximum of 9x^(2)-12xy costheta + 4y^(2) is

If cos^(-1)((x)/(3))+cos^(-1)((y)/(2))=(theta)/(2) , then the value of 4x^(2)-12xy cos((theta)/(2))+9y^(2) is equal to :

If x=a sin theta and y=b cos theta , then prove : (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

Let cos^-1(x/a)+cos^-1(y/b)=alpha thenAnswer the following questions (A) x^2/a^2+y^2/b^2+(2xy)/(ab) cos alpha = sin^2 alpha (B) x^2/a^2-y^2/b^2+(2xy)/(ab) cos alpha = sin^2 alpha (C) x^2/a^2+y^2/b^2-(2xy)/(ab) cos alpha = sin^2 alpha (D) x^2/a^2-y^2/b^2-(2xy)/(ab) cos alpha = sin^2 alpha

If cos^(-1)(x/a) + cos^(-1) (y/b) = alpha show that : (x^2)/(a^2) - (2xy)/(ab) cos alpha + (y^2)/(b^2) = sin^(2) alpha .

If cos^(-1) . x/a - sin^(-1). y/b = theta (a , b , ne 0) , then the maximum value of b^(2) x^(2) + a^(2) y^(2) + 2ab xy sin theta equals

If x = a cos theta ,y = b sin theta , then find the value of b^(2) x^(2) + a^(2) y^(2) - a^(2) b^(2) .