" 5."sin[(x)/(1+sqrt(x))]

sin^(-1)[sqrt(x/(a+x))]=

(d)/(dx) Tan^(-1)[(sqrt(1+sinx) - sqrt(1-sin x))/(sqrt(1+sin x) + sqrt(1-sin x))]=

Differentiate w.r.t.x the function cot^(^^)(-1)[(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)(sqrt(1-sin x))],0

If x in[(sqrt(3))/(2), 1] then [sin^(-1){(x)/(sqrt(2))+(sqrt(1-x^(2)))/(sqrt(2))}-sin^(-1)x]=

(d)/(dx) [ 2 cot^(-1) ((sqrt(1+ sin x) + sqrt(1-sin x))/(sqrt(1+ sin x) - sqrt(1-sin x)))]=

If x and y are acute angles such that sin x=(1)/(sqrt(5)) and sin y=(1)/(sqrt(10)) prove that x+y=(pi)/(4)

lim_(x to 0) (x +2 sin x)/(sqrt(x^(2)+2 sin x + 1)-sqrt(sin^(2) x - x+ 1)) is

Differentiate (sin x)^(5)+sin^(-1)sqrt(x)

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