# Integral containing two separate sin functions

#### blorpinbloo

Hey all, my integration is a bit rusty so I'm having trouble with integrating a function thats something like:

sin(yx)sin(zx)dx

How would I go about a problem like that?

#### Also sprach Zarathustra

Hey all, my integration is a bit rusty so I'm having trouble with integrating a function thats something like:

sin(yx)sin(zx)dx

How would I go about a problem like that?
Use the following trigonometric identity:

$$\displaystyle sin(a)sin(b)=\frac{1}{2}[cos(a-b)-cos(a+b)]$$

#### Prove It

MHF Helper
Hey all, my integration is a bit rusty so I'm having trouble with integrating a function thats something like:

sin(yx)sin(zx)dx

How would I go about a problem like that?
It needs to be asked if $$\displaystyle y$$ and/or $$\displaystyle z$$ are functions of $$\displaystyle x$$ or if they are independent of $$\displaystyle x$$?

AllanCuz

#### slider142

Assuming y and z are not functions of x, the integral is independent of these variables and y and z may be treated as constants. Then integration by parts (applied twice to get a multiple of the original integrand) makes short work of this integral.
Otherwise, you need to know those functions of x.