Trigonometric equation help !

[Ximei]

I need help solving this equation
\(\displaystyle cos5x+cos7x=sin2x\)
On the left side i got to \(\displaystyle 2cos6xcox\) , but
I don't know what to do with \(\displaystyle sin2x\)
Any help would be appreciated

 

[Deleted member 4993]

I need help solving this equation
\(\displaystyle cos5x+cos7x=sin2x\)
On the left side i got to \(\displaystyle 2cos6xcox\) , but
I don't know what to do with \(\displaystyle sin2x\)
Any help would be appreciated

\(\displaystyle sin(2x) \ \ = \ \ 2 \cdot \ sin(x) \ \cdot \ cos(x)\)

 

[Ximei]

Thank you
But after I use that
I get to \(\displaystyle cos6x=sinx\) and again I don't know what to do with \(\displaystyle sinx\)
I tried writing it like this \(\displaystyle cos6x - cos (\pi/2 - x) = 0\)
and using this

but it didn't get me anywhere
Any ideas ?

 

[Deleted member 4993]

Thank you
But after I use that
I get to \(\displaystyle cos6x=sinx\) and again I don't know what to do with \(\displaystyle sinx\)
I tried writing it like this \(\displaystyle cos6x - cos (\pi/2 - x) = 0\)
and using this

but it didn't get me anywhere
Any ideas ?

I think you are in the correct path:

\(\displaystyle Sin\left (\frac{\theta + \phi}{2}\right ) = 0 = Sin(n\pi )\)

\(\displaystyle \left (\frac{\theta + \phi}{2}\right ) \ \ = \ \ n \cdot \pi\)

Did you continue this way?