[2sin^(-1)x=sin^(-1)(2x sqrt(1-x^(2)))],[th ln x=]

Prove that 2sin^(-1)x=sin^(-1)[2x sqrt(1-x^(2))]

If sin^(-1)x+sin^(-1)(1-x)=sin^(-1)sqrt(1-x^(2)), then x is equal to

Prove that : 2 sin^-1 x = sin^-1 (2x sqrt(1-x^2)), |x| le (1/(sqrt2)

If y=(x sin^(-1)x)/(sqrt(1-x^(2)))+log sqrt(1-x^(2)), then prove that (dy)/(dx)=(sin^(-1)x)/((1-x^(2))^((3)/(2)))

If sin^-1x + sin^-1(1-x) = sin^-1sqrt[1-x^2] ,then x is equal to

(tan^(-1)x)/(sqrt(1-x^(2))) withrespectto sin ^(-1)(2x sqrt(1-x^(2)))

If y={(log)cos x sin x}{(log)_(sin x)cos x}^(-1)+sin^(-1)((2x)/(1+x^(2))) fin d (dy)/(dx)atx=(pi)/(4)

If y={log_(cos x)sin x}{log_(sin x)cos x)^(-1)+sin^(-1)((2x)/(1+x^(2))) find (dy)/(dx) at x=(pi)/(4)

If x in[(sqrt(3))/(2), 1] then [sin^(-1){(x)/(sqrt(2))+(sqrt(1-x^(2)))/(sqrt(2))}-sin^(-1)x]=

Find the greatest & least value of f(x)=sin^(-1).(x)/(sqrt(x^(2)+1))-ln x in [(1)/(sqrt(3)), sqrt(3)] .