# How many waves have superposed?

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The displacement of particle executing periodic motion is given as :
$y= 4 cos^2(t/2)sin(1000t)$
The above expression may be considered to be result of superposition of :

1. 2 waves
2. 3 waves
3. 4 waves
4. 5 waves

I tried this by changing $cos$ function,
as $4 [(1+cost)/2 ] sin1000t$
but now after I think its superposition of 2 waves but given answer is 3 waves , then how should Interpret the number waves ?

$$4[(1+cost)/2]sin1000t$$$$2\sin 1000t + 2\cos t \sin 1000t$$
Using $2\sin a \cos b =\sin (a+b)/2 + \sin(a-b)/2$
$$2\sin 1000t + \sin 1001t/2 +\sin 999t/2$$