How to Solve a Tricky Integration Using Prosthaphaeresis Formulas?

[yungman]

I need help how to solve this integration:

$$\int_0^h sin[\beta(h-z)] \; cos(\beta\;z \; cos \theta)\; dz$$

I tried substitution of $\;U=\beta(h-z)\;$ and going nowhere. $\; cos(A+B)\;$ type of method won't work either because you can't get A and B out of this. Please help.

Thanks

Alan

 

[LCKurtz]

I need help how to solve this integration:

$$\int_0^h sin[\beta(h-z)] \; cos(\beta\;z \; cos \theta)\; dz$$

I tried substitution of $\;U=\beta(h-z)\;$ and going nowhere. $\; cos(A+B)\;$ type of method won't work either because you can't get A and B out of this. Please help.

Thanks

Alan

Use one of the prosthaphaeresis formulas:

$$\sin\theta\cos\phi=\frac{\sin(\theta+\phi)+\sin(\theta -\phi)}{2}$$

 

[yungman]

Use one of the prosthaphaeresis formulas:

$$\sin\theta\cos\phi=\frac{\sin(\theta+\phi)+\sin(\theta -\phi)}{2}$$

Sorry to acknowledge so late, took me a while to work it out.

Thanks