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Hi, how to find the general solution(s) of the following equation:

$$cos(\theta)=sin(2\theta)$$ (in radians).

and:

Show that the general solution of $$tan(3x-\frac{\pi}{4})=tan(x)$$ is $$x=\frac{(4n+1)\pi}{8}$$ (n is an integer).

Aug 3, 2021

e.g. i got $$x=\frac{(8n+5)\pi}{8}$$ this satisfies $$tan(3x-\frac{\pi}{4})=tan(x)$$ for all n, but the question says $$x=\frac{(4n+1)\pi}{8}$$ is the answer which is not equal to what I got (although both satisfies the equation). Does anyone have an explanation please?