If `cos^(-1).(x)/(2) + cos^(-1).(y).(3) = (pi)/(6)`, then prove that `(x^(2))/(4) - (xy)/(2sqrt3) + (y^(2))/(9) = (1)/(4)`

sin ^ (- 1) ((x) / (3)) + sin ^ (- 1) ((y) / (4)) = (pi) / (6) then prove that (x ^ (2)) / (9) + (y ^ (2)) / (16) + (xy) / (4sqrt (3)) = (1) / (4)

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 +cos^(-1)y +cos^(-1)z =pi , then prove that x^(2)+y^(2)+z^(2)+2xyz=1 .

If y=(cos^(-1)x)^(2) , then prove that : (1-x^(2))y_(2)-xy_(1)-2=0 .

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

If cos^(-1) x + cos^(-1) y + cos^(-1) z = pi , prove that x^(2) + y^(2) + z^(2) + 2xyz = 1

If cos^(-1) x + cos^(-1) y + cos^(-1) z = pi , prove that x^(2) + y^(2) + z^(2) + 2xyz = 1

If cos^(-1)""x/2+cos^(-1)""y/3=pi/6 , then value of x^2/4-(xy)/(2sqrt3)+y^2/9 a) 3/4 b) 1/2 c) 1/4 d)None of these

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