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

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

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

solve : sin ^(-1) ""((x)/(sqrt(1+x^(2))))-sin ^(-1)((1)/(sqrt(1+x^(2))))= sin ^(-1) ((1+x)/(1+x^(2)))

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

y=sin^(-1)((x)/(sqrt(1+x^(2))))+cos^(-1)((1)/(sqrt(1+x^(2))))

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

Prove that 2tan^(-1)((1)/(2))+tan^(-1)((1)/(7))=sin^(-1)((31)/(25sqrt(2)))

Prove that 2tan^(-1)(1/2)+tan^(-1)(1/7)=sin^(-1)((31)/(25sqrt(2)))

If y=sin^(-1)(xsqrt(1-x)+sqrt(x)sqrt(1-x^2)) and (dy)/(dx)=1/(2sqrt(x(1-x)))+p , then p is equal to 0 (b) 1/(sqrt(1-x)) sin^(-1)sqrt(x) (d) 1/(sqrt(1-x^2))

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