Definite integration involving multiple angle of sine.

[anirudhsharma1]

pi
∫sin^2(nx)/sin^2(x) dx
0

I tried using mathematical induction and did arrive at the correct result but was wondering if a better method could be used to solve it?

 

[Mandelbroth]

pi
∫sin^2(nx)/sin^2(x) dx
0

I tried using mathematical induction and did arrive at the correct result but was wondering if a better method could be used to solve it?

How do you use induction here? You haven't even given us a result!

 

[anirudhsharma1]

putting n=1,n=2
we get pi, and pi as the result
so i generalised it for 'n'.
thats the reason i asked for the solution because this is definitely an improper method.

 

[Mandelbroth]

putting n=1,n=2
we get pi, and pi as the result
so i generalised it for 'n'.
thats the reason i asked for the solution because this is definitely an improper method.

Are you confused about what induction means?