" 95) "quad " 18."(x cos^(-1)x)/(sqrt(1-x^(2)))

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

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

cos^(-1)((2sqrt(x))/(1+x))

cos^(-1)((sqrt(1+x)-sqrt(1-x))/(2))

If y=(x cos^(-1)x)/(sqrt(1-x^(2)))-log sqrt(1-x^(2)), then prove that (dy)/(dx)=(co^(1-x)x)/((1-x^(2))^((3)/(2)))

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

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

If 1/(sqrt(2))