If $\sin x-\sin y=\frac{27}{65}$ and $\cos x-\cos y=\frac{-21}{65}$, then $\sin (x+y)=$

If $\left(\frac{\sin 3 \theta}{\sin \theta}\right)^2-\left(\frac{\cos 3 \theta}{\cos \theta}\right)^2=a \cos b \theta$, then $a: b=$

An aeroplane is flying at a constant speed, parallel to the horizontal ground at a height of 5 kms . A person on the ground observed that the angle of elevation of the plane is changed from $15^{\circ}$ to $30^{\circ}$ in the duration of 50 seconds, then the speed of the plane (in kmph ) is