I reckon you can put this on your mistake book, when doing trig expansions the solution is
![](https://latex.codecogs.com/png.latex?\bg_white \cos{(A+B)}=\cos{A}\cos{B}-\sin{A}\sin{B})
note you multiply the
![](https://latex.codecogs.com/png.latex?\bg_white \cos)
and
![](https://latex.codecogs.com/png.latex?\bg_white \sin)
terms instead of adding them. Eg. we are told that
![](https://latex.codecogs.com/png.latex?\bg_white \cos{(\theta-\theta)}=1=\cos^{2}{\theta}+\sin^{2}{\theta}{)
, not
![](https://latex.codecogs.com/png.latex?\bg_white \cos{\theta}+\cos{\theta}+\sin{\theta}+\sin{\theta}=2\cos{\theta}+2\sin{\theta})
.
yashbb's mistake is very clear and is very common for newcomers to trig expansion, or people who have not done trig expansion for a long time, he understands the concept that
![](https://latex.codecogs.com/png.latex?\bg_white \cos{(A+B)}=\cos{A}\cos{B}-\sin{A}\sin{B})
but his misstep is that
![](https://latex.codecogs.com/png.latex?\bg_white \cos{(A+B)}=\cos{A}+\cos{B}+\sin{A}+\sin{B})
which comes from doing
![](https://latex.codecogs.com/png.latex?\bg_white 5x(x-2)=5x^{2}-10x)
, a pretty common mistake that can easily be corrected in the student's journey to mathematical proficiency.
A good mistake to make because you get to see where you went wrong early. Albeit mathematics is a learning experience.