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

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

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

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

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

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

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 the following functions in the simplest from : sin^(-1)(x^(2)sqrt(1-x^(2))+xsqrt(1-x^(4)))

Write the following functions in the simplest from : sin^(-1)(x^(2)sqrt(1-x^(2))+xsqrt(1-x^(4)))

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

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