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

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

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 :

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

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

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

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)