If `0ltxltpi/2` prove that `sqrt(tanx+sinx)+sqrt(tanx-sinx)=2sqrt(tanx)cos (pi/4-x/2)`

Find int(sqrt(cotx)+sqrt(tanx))dx

Prove that: int_0^(pi/4)(sqrt(tanx)+sqrt(cotx))\ dx=sqrt(2)pi/2

Show that: int_0^(pi/2) "sqrt(tanx) + sqrt(cotx) = sqrt(2)pi

The value of lim_(xto0^(+))(-1+sqrt((tanx-sinx)+sqrt((tanx-sinx)+sqrt((tanx-sinx)+…oo))))/(-1+sqrt(x^(3)+sqrt(x^(3)+sqrt(x^(3)+…oo)))) is

Prove that : int_(0)^(pi//2) (sqrt(tanx))/(sqrt(tanx +sqrt(cotx)))dx=(pi)/(4)

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

Prove that: cot^(-1){(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))}=pi/2-x/2 , if pi/2 < x < pi

Evaluate: int(sqrt(tanx)+sqrt(cotx))dx

Evaluate: int(sqrt(tanx)+sqrt(cotx))dx

int(sec^(2)x)/(sqrt(tanx))dx