if y = `sin^-1x`, show that `(1-x^2) y_2 = xy_1`

If y = tan^(-1)x show that (1+x^2)(d^2y)/(dx^2) + 2x(dy)/(dx) = 0

If y=sin^(-1) x , show that ((dy)/(dx))_(x=0)=1 .

If x + y + z =xyz,show that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/(1-x^2).(2y)/(1-y^2).(2z)/(1-z^2)

If sin^-1 x +sin^-1 y + sin ^-1 z=pi , prove that xsqrt(1-x^2)+ysqrt(1-y^2)+zsqrt(1-z^2)=2xyz

If sin^-1 x+sin^-1 y +sin^-1 z=pi/2 , prove that x^2+y^2+z^2+2xyz=1 .

If sin^-1 x+sin^-1 y=theta , prove that x^2+y^2+2xycostheta=sin^2theta

If 3x + 2y = -1 , then prove that 27x^3+8y^3+1-18xy = 0

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