an interesring integral with an interesting method

[@MASHabibi-d2d]

Thanks for an other video master.

[@holyshit922]

I have integral with interesting result
\int_{\theta}^{\pi}\frac{\sin{\left(\left(n+\frac{1}{2}
ight)t
ight)}}{\sqrt{2\left(\cos{\left(\theta
ight)} - \cos{\left(t
ight)}
ight)}}dt
I have no problems with calculating this integral but I have limited recording time and I cant to present solution
Hints
Use trigonometric identities like
sin(x+y)=sin(x)cos(y)+cos(x)sin(y)
2sin(x)cos(y)=sin(x+y)+sin(x-y)
and integration by parts to derive recursive relation
Calculate base cases for recursion
Use generating function to derive explicit formula for integral in terms of a finite sum

[@arantheo8607]

Favorite method : the last one

[@holyshit922]

Euler's substitution sqrt(4+x^2)=u ± x
You can choose the sign

[@ahmedsabri-ng2xx]

an interesring integral