I have an equation of $\cos Ax \cos Bx = c$ where $A$,$B$ and $c$ are known constants - how to solve for unknown $x$?
2026-03-25 23:37:14.1774481834
Solving product of two cosine terms
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To expand on my comment, let's look at a simple example: $$ \cos2x\cos3x=.1 $$ We have $$ \cos2x=2\cos^2x-1,\qquad\cos3x=4\cos^3x-3\cos x $$ so our equation becomes $$ (2\cos^2x-1)(4\cos^3x-3\cos x)=.1 $$ Multiply out, and let $u=\cos x$, we get $$ 8u^5-10u^3+3u=.1 $$ a fifth-degree equation, and there is no algebraic formula for solving those – one must resort to numerical methods.