if angle B and angle Q acute angles such that sin B = sin Qthen prove that angle B=angle Q

It is given that sin B = sin Q

Clearly, since B and Q are acute angles, angle B = angle Q.

(As sine of two acute angles will be equal if and only if they are both equal)

 

You can prove this also by considering a right triangle ABQ.

Since, B and Q are acute angles, angle B is right angle.

Then, sinQ = AB/AQ

sin B = BQ/ AQ

 

Now, sin B = sin Q implies, AB = BQ

This gives angle B = angleQ