I need to solve this simple transcendental equation, but I don't exactly know how.
$cos(x - 2y) + 8x + 4y = 0$
I mean, I think I've never learnt any method to try solving an equation like this. The only way I can think of is the bisection method, but it would be quite long. Is there something I'm missing?
I'm sorry, I'm quite new to exercises of this kind.
Let $x-2y=z.$ Then $0=\cos z+8x+4y=\cos z+8z+20y,$ so $$y=-(8z+\cos z)/20\;..... (1)$$ and $$x=z+2y=z-(8z+\cos z)/20\;..... (2)$$ Putting any $z$ into $(1)$ and $(2)$ will give a solution for $x,y.$
Don't try to find a simple formula for $y$ in terms of $x,$ or vice-versa. There isn't one.