If `cos ^(-1) ""(x)/(2) + cos ^(-1) "" (y)/(3) = theta, ` then prove that `9x ^(2) - 12 xy cos theta + 4y ^(2) = 36 sin ^(2) theta`

If "cos"^(-1) x/(2)+"cos"^(-1) y/(3)=theta , then prove that 9x^(2)-12xy " cos "theta+4y^(2)=36" sin "^(2)theta

If cos^(-1)(x/2)+cos^(-1)(y/3) = theta , prove that 9x^2- 12xycostheta+ 4y^2= 36 sin^(2)theta

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) =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/a+cos^(-1)""y/b=theta , Prove that x^(2)/a^(2)-(2xy)/(ab)costheta+y^(2)/b^(2)=sin^(2)theta .

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 cos^(-1)x/2+cos^(-1)y/3=theta , then 9x^2-12 x ycostheta+4y^2 is equal to (a) 36 (b) -36\ sin\ ^2theta (c) 36\ sin\ ^2theta (d) 36\ cos\ ^2theta

If x +y= 3-cos4theta and x-y=4sin2theta then

If 2 cos theta = x + (1)/(x), prove that 2 cos 3 theta = x ^(3) + (1)/(x ^(3)).