Write each of the following in the simplest form: `sin^(-1){(sqrt(1+x)+sqrt(1-x))/2},\ \ 0

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

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

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

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

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

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

Express each of the following in the simplest form: tan^(-1){sqrt((1-cosx)/(1+cosx))}, -pi

Write the following function in the simplest form: tan^(-1)sqrt((1-cos x)/(1+cos x))

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))]