`sin^(-1) (2xsqrt(1-x^2)), x in [1/sqrt2,1]` is equal to

Prove the following : sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,x in[-1/sqrt2,1/sqrt2]

The value of sin^(-1)[xsqrt(1-x)+sqrt(x)sqrt(1-x^2)] is equal to

The value of sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2)] is equal to

The value of sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2)] is equal to

The value of sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2)] is equal to

The value of sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2)] is equal to

Differentiate tan^(-1)(x/(sqrt(1-x^2))) with respect to sin^(-1)(2xsqrt(1-x^2)), if -1/(sqrt(2)) < x< 1 /(sqrt(2))

Write the following functions in the simplest from : sin^(-1)(2xsqrt(1-x^(2))),-1/sqrt2lexle1/sqrt2

y = sin^(-1)(2xsqrt(1 - x^2)), -1/(sqrt2) lt x lt 1/(sqrt2)

Find dy/dx in the following : y=sin^(-1)(2xsqrt(1-x^(2))),-1/sqrt2ltxlt1/sqrt2 .