If `cos^(-1) x - cos^(-1).(y)/(2) = alpha`, then `4x^(2) - 4xy cos alpha + y^(2)` is equal to

If cos^(- 1)x-cos^(- 1)(y/2)=alpha then 4x^2-4xycosalpha+y^2=

If cos^(-1)x-cos^(-1)y/2=alpha,t h e n4x^2-4x ycosalpha+y^2 is equal to 4 (b) 2sin^2alpha (c) -4sin^2alpha (d) 4sin^2alpha

If cos ^(-1)((3)/(5)), beta = tan ^(-1)((1)/(3)) , where -1 le x le 1, -2 le y le 2, x le (y)/(2) , then for all x,y, 4x^(2) - 4xy cos alpha + y^(2) is equal to

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

If cos^(-1) (x/2) + cos^(-1) (y/3) =alpha then prove that 9x^2-12xycosalpha+4y^2=36sin^2alpha .

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 + cos^(-1)y + cos^(-1)z = pi, then xy + yz +zx is equal to

If cos^(-1)x + cos^(-1)y + cos^(-1)z = 3pi, then xy + yz +zx is equal to

If cos^(-1)(x/a)+cos^(-1)(y/b)=alpha, prove that (x^2)/(a^2)-2(x y)/(a b)cosalpha+(y^2)/(b^2)=sin^2alpha

If cos^(-1)(x/a)+cos^(-1)(y/b)=alpha, prove that (x^2)/(a^2)-2(x y)/(a b)cosalpha+(y^2)/(b^2)=sin^2alpha