Prove that the value of sin3x/cos2x is positive in (13pi/48,14pi/48)?

 First lets prove that sin3x/cos2x=(2 sin(3 x) cos(2 x))/(cos(4 x) +1)

Cross multiply:

sin(3 x) (cos(4 x) +1)=2 cos(2 x)^2 sin(3 x)

Dividing both sides by sin(3 x):

cos(4 x) +1=2 cos(2 x)^2

cos(2 x)^2 =1/2 (cos(4 x) +1):

cos(4 x) +1=2 (cos(4 x) +1)/2

(2 (cos(4 x) +1))/2 =cos(4 x) +1:

cos(4 x) +1=cos(4 x) +1

The left hand side and right hand side are equal.

So as in (2 sin(3 x) cos(2 x))/(cos(4 x) +1): sin3x,cos2x,cos4x are positive(as all angles lie in first quadrant as it is asked between 13pi/48 to 14pi/48)

Therefore sin3x/cos2x is always positive in (13pi/48,14pi/48).