If `pi/2 lt x lt pi`, then find `d/dx(sqrt((1+cos2x)/2))`

Comprehension 2 (Q.No 4 to 6) It is known that sqrt(tanx)+sqrt(cotx)={{:(sqrt(sinx)/sqrt(cosx)+sqrt(cosx)/sqrt(sinx), if 0ltxltpi/2),(sqrt(-sinx)/sqrt(cosx)+sqrt(-cosx)/sqrt(-sinx),if pi lt x lt (3pi)/(2)):} d/(dx)(sqrt(tanx)-sqrt(cotx)) =1/2(sqrt(tanx)+sqrt(cotx))(tanx+cotx), AA in (0,pi,2) uu (pi,(3pi)/2) and d/(dx)(sqrt(tanx)+sqrt(cotx))=1/2(sqrt(tanx)-sqrt(cotx))(tanx+cotx), AA x in (0,pi/2) uu (pi, (3pi)/(2)) . Value of the integral I=int(sqrt(tanx)+sqrt(cotx)) dx, where x in (0,pi/2) , is

(a) Find d/dx (log sqrt (x^2+a^2))=?

If sin x = 1/4 , pi/2 lt x lt pi , find the values of cos\ x/2 and tan\ x/2 .

If cos x + sin x = a , (- (pi)/(2) lt x lt - (pi)/(4)) , then cos 2 x is equal to

If x in (0,pi/2),t h e ns howt h a t d/(dx)cos^(-1){7/2(1+cos2x)+(sqrt(sin^2x-48cos^2x))sinx} =1+(7sinx)/sqrt(sin^2-48cos^2x)

if cos x= (-sqrt(15))/(4) " and " (pi)/(2) lt x lt pi find the value of sin x .

Differentiate sinsqrt(x) + cos^(2)sqrt(x)

Differentiate sinsqrt(x) + cos^(2)sqrt(x)

Differentiate the following functions with respect to x : tan^(-1){sqrt((1+cosx)/(1-cosx))} , 0< x < pi

Differentiate the following functions with respect to x : tan^(-1){sqrt((1+cosx)/(1-cosx))} , 0< x < pi