`2(1+sin^2(x-1))=2^(2x-x^2)`

Sin^(-1) 2x √(1-x^2)

tan((1)/(2) sin ^(-1)""(2x)/(1+x^(2))+(1)/(2)cos^(-1)((1-x^(2))/(1+x^(2))))=(2x)/(1-x^(2))(|x|ne 1)

If x(3-x)<=2 then sin^(-1)(x)+sin^(-1)(x^(2))+......+sin^(-1)(x^(10))=

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

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

sin^(-1) ((2x)/(1 + x^(2)))

sin((1+x^(2))/(1-x^2))

if x^(2) !=npi+1 , ninN then int x sqrt((2sin(x^(2)-1)-sin2(x^(2)-1))/(2sin(x^(2)-1)+sin2(x^(2)-1))) dx is equal to (a) In cos ((x^(2)-1)/(2))+c (b) (1)/(2)In cos ((x^(2)-1)/(2))+c (c) In sec ((x^(2)-1)/(2))+c (d) (1)/(2)In sec ((x^(2)-1)/(2))+c

Prove that sin^(-1)((2x)/(1+x^2))=tan^(-1)((2x)/(1-x^2))

Prove that sin^(-1)((2x)/(1+x^2))=tan^(-1)((2x)/(1-x^2))