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

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

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

Write the following function in the simplest form: tan^(-1)((sqrt(1+x^2)-1)/x ), x!=0

Write the following functions in the simplest form: (i) sin^(-1){x/(sqrt(x^2+a^2))} (ii) cos^(-1){x/(sqrt(x^2+a^2))}

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

int(sqrt(1-x^(2))+sqrt(1+x^(2)))/(sqrt(1-x^(4)))dx=

Write the following function in the simplest form: tan^(-1)(1/(sqrt(x^2-1))),|x|>1

Write each of the following in the simplest form: cot^(-1){a/(sqrt(x^2-a^2))},|x|> a

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

Write each of the following in the simplest form: tan^(-1){sqrt(1+x^2)-x},\ \ x in R (ii) tan^(-1){(sqrt(1+x^2)-1)/x},\ \ x!=0