[[1,(i),tan^(-1)(x)/(sqrt(a^(2)-x^(2)))=sin^(-1)(x)/(a)]quad " INCERTI "

Prove that tan^(-1) {(x)/(a + sqrt(a^(2) - x^(2)))} = (1)/(2) sin^(-1).(x)/(a), -a lt x lt a

Prove that tan^(-1) {(x)/(a + sqrt(a^(2) - x^(2)))} = (1)/(2) sin^(-1).(x)/(a), -a lt x lt a

int (tan (sin^(-1)x))/(sqrt(1-x^(2)))dx=

Prove that tan^(-1)((x)/(sqrt(a^(2)-x^(2))))="sin"^(-1)(x)/(a)=cos^(-1)((sqrt(a^(2)-x^(2)))/(a)) .

Prove that tan^(-1){(x)/(a+sqrt(a^(2)-x^(2)))}=(1)/(2)(sin^(-1)x)/(a),-a

Prove that tan^(-1){x/(a+sqrt(a^2-x^2))}=1/2sin^(-1)(x/a) ,-a lt x lt a

prove that tan^(-1)((x)/(1+sqrt(1-x^(2)))]=(1)/(2)sin^(-1)x

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

(iv) If y=tan^(-1)(x/(1+sqrt(1-x^(2))))+sin(2tan^(-1)sqrt((1-x)/(1+x))) , then find (dy)/(dx) for x epsilon(-1,1)

Prove that tan^(-1){x/(a+sqrt(a^2-x^2))}=1/2sin^(-1)x/a ,-a lt x lt a