Check the monotonicity of f(x) =[ x/ sin x] in (0, p/2)

f'(x)=sinx-xcosx/(sinx)^2

for small x, sinx=x
f'(x)=x(1-cos x)> greater than zero
for higher values of x, also f'(x)>0, hence the function f(x) is monotonically increasing.

Sher Mohammad
B.Tech, IIT Delhi