" (v) "cos^(-1)sqrt((sqrt(1+x^(2))+1)/(2sqrt(1+x^(2))))quad " (NCERT) "

show that , (1) /(2) tan ^(-1) x = cos^(-1) sqrt((1+sqrt(1+x^(2)))/(2sqrt(1+x^(2)))).

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

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

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

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

Derivative of tan ^(-1) ((sqrt( 1+x^(2))-1)/( x)) w.r.cos ^(-1) sqrt((1+sqrt( 1+x^(2)))/( 2sqrt(1+x^(2)))) is

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))))

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