`y=sin^(-1) (2^(x+1)/(1+4^x))`

If y = sin^(-1) x^2 sqrt(1 - x^2) + xsqrt(1 - x^4) , show that (dy)/(dx) - (2x)/(sqrt(1 - x^4)) = 1/(sqrt(1 - x^2))

If x=sin(2tan^(-1)2)and y=sin((1)/(2)tan^(-1).(4)/(3)) , then prove that y^2 = 1 - x

If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then prove that (1-x^2)y_2-xy_(1)-4=0.

If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then prove that (1-x^2)y_2-xy_(1)-4=0.

If sin^(-1)x +sin^(-1)y+sin^(-1)z=pi then x^(4)+y^(4)+z^(4)+4x^(2)y^(2)z^(2)=

If y=sin^(-1)x/sqrt(1-x^2) prove that (1-x^2)y^2=(sin^(-1)x)^2

If y=sin^(-1)x/sqrt(1-x^2) prove that (1-x^2)y_1-xy=1