" 14."sin^(-1)(sqrt((1-x)/(2)))

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

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

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

The complete solution set of the equation sin^(-1) sqrt((1+x)/(2))-sqrt(2-x)=cot^(-1)(tan sqrt(2-x))-sin^(-1) sqrt((1-x)/(2)) is :

Prove the following: sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2))

Show that, sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/sqrt2lexle1/sqrt2

Write each of the following in the simplest form: (i) sin^(-1){(sqrt(1+x)+sqrt(1-x))/2},\ \ 0 < x <1 (ii) sin{2tan^(-1)(sqrt((1-x)/(1+x)))}