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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
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I get the general solution and when testing it, like n=1 , n=2 , n=99 etc.. it works when substituiting in the equation. However, the general solution is not equal to what is required. 
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?

 Aug 3, 2021

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