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

Write into the simplest form: cot^(-1)(sqrt(1+x^(2))+x)

Write the simplest form : tan^(-1)(1/sqrt(x^2 -1)) , |x|gt1

Write the simplest form : cot^(-1) [(sqrt(1+sinx)+sqrt(1-sin x))/(sqrt(1+sinx)-sqrt(1-sin x)]], x epsilon [0, pi/4]

Write the simplest form : tan^(-1)( (sqrt(1+x)-sqrt(1-x))/(sqrt(1+x) + sqrt(1-x))); (-1)/sqrt(2) le x le 1

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

Write simplest form: sin^(-1)(x^(2)sqrt(1-x^(2))+x sqrt(1-x^(4)))

Write the following function in the simplest form: sin^(-1)[x sqrt(1-x)-sqrt(x)sqrt(1-x^(2))]

Differential coefficient tan^(-1)((sqrt(1-x^(2)-1))/(x)) with respect to cos^(-1)sqrt((1+sqrt(1+x^(2)))/(2sqrt(1-x^(2))))

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