Solve `tanx >cotx ,` where `x in [0,2pi]dot`

Find (dy)/(dx) for y=sin^(-1)(cosx), where x in (0,2pi)dot

Find (dy)/(dx) for y=sin^(-1)(cosx), where x in (0,2pi)dot

Find the number of roots of the equation tan(x+pi/6)=2tanx ,forx in (0,3pi)dot

Find the number of roots of the equation tan(x+pi/6)=2tanx ,forx in (0,3pi)dot

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

Let f(x)=min.[tanx, cotx, 1/sqrt(3)], x in [0, pi/2] . If the area bounded by y=f(x) and x-axis is ln(a/b)+pi/(6sqrt(3)) , where a,b are coprimes. Then ab =…..

Using mean value theorem, prove that tanx > x for all x(0,pi/2)dot

int_0^a log (cota+ tanx)dx where a in (0,pi/2) is

Prove that f(x)=(sinx)/x is monotonically decreasing in [0,pi/2]dot Hence, prove that (2x)/pi

Prove that f(x)=(sinx)/x is monotonically decreasing in [0,pi/2]dot Hence, prove that (2x)/pi