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

Differentiate: e^(cos^(-1)sqrt(1-x^(2))

Find the range of f(x)=sqrt(cos^(-1)sqrt((1-x^2))-sin^(-1)x)

Write the simplest form : cos^(-1)(sqrt(((sqrt(1+x^2) +1)/(2sqrt(1+x^2))))

If (1)/(sqrt2) lt x lt 1 , then prove that cos^(-1) x + cos^(-1) ((x + sqrt(1 - x^(2)))/(sqrt2)) = (pi)/(4)

Evaluate the following limit: (lim)_(x->1/(sqrt(2)))(cos^(-1)(2xsqrt(1-x^2)))/(x-1/(sqrt(2)))

Find the range of f(x)=cos^(-1)((sqrt(1+2x^2))/(1+x^2))

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

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

Evaluate: inttan^(-1){sqrt(((1-cos2x)/(1+cos2x)))}

Prove that cos^(-1) (sqrt(1/3))-cos^(-1) (sqrt((1)/(6)))+cos^(-1) ((sqrt(10)-1)/(3sqrt2))=cos^(-1) (2/3)