if sin(pie/4 cotA) = cos(pie/4 tanA) then find the general solution of A

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{We} \mathrm{have} \\ \sin \left(\frac{\mathrm{\pi }}{4}\mathrm{cotA}\right)=\cos \left(\frac{\mathrm{\pi }}{4}\mathrm{tanA}\right)....\left(\mathrm{i}\right) \\ \mathrm{We} \mathrm{know} \mathrm{that} \cos \left(\frac{\mathrm{\pi }}{4}\right)=\sin \left(\frac{\mathrm{\pi }}{4}\right)=\frac{1}{\sqrt{2}} \\ \mathrm{Hence} \left(\mathrm{i}\right) \mathrm{is} \mathrm{possible} \mathrm{when} \\ \mathrm{tanA}=\mathrm{cotA}=1 \\ \mathrm{i}.\mathrm{e}. \\ \mathrm{tanA}=1 \\ \Rightarrow \mathrm{tanA}=\tan \left(\frac{\mathrm{\pi }}{4}\right) \\ \Rightarrow \mathrm{A}=\mathrm{n\pi }+\frac{\mathrm{\pi }}{4}, \mathrm{where} \text{'}\mathrm{n}\text{'} \mathrm{is} \mathrm{any} \mathrm{integer}. \end{gathered}$$
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