(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))=?

Prove that cot^(-1) ((sqrt(1+sin x) +sqrt(1-sin x))/(sqrt(1+sin x) -sqrt(1-sinx)))=(x)/(2), x in (0, (pi)/(4)) .

Prove that : cot^-1[(sqrt(1+sin x) + sqrt(1-sin x))/(sqrt1+sin x + sqrt(1-sin x))] = x/2, x in (0, pi/4)

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

Find the derivate of : y= tan^-1(frac(sqrt(1+sinx)- sqrt(1 - sin x))(sqrt(1 +sinx)+sqrt(1-sin x)))

Prove that cot^(-1)((sqrt(1+sin)+sqrt(1-sin x))/(1sqrt(1+sin)-sqrt(1-sin x)))=(x)/(2);x in(0,(pi)/(4))

If y=tan^(-1) [(sqrt(1+sinx)-sqrt(1-sin x))/(sqrt(1+sin x)+sqrt(1-sin x)]] where 0 lt x lt pi/2 find (dy)/(dx)

Prove that tan^(-1)((sqrt(1+x)-sqrt(1-sin x))/(sqrt(1+x)-sqrt(1-sin x)))=(pi)/(4)-(1)/(2)cos^(-1),-(1)/(sqrt(2))<=x<=1

sqrt((1+sin x)/(1-sin x))

lim_(x rarr0)(sqrt(1+sin x)-sqrt(1-sin x))/(x)