Find the general solutions of the following equations: 3x+ 2x=0 - Vidyadip

Question

Find the general solutions of the following equations: $\sin3\text{x}+\cos2\text{x}=0$

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Answer

$\cos(2\text{x})=-\sin(3\text{x})$$=-\cos(\frac{\pi}{2}-3\text{x})$
$=\cos(\frac{\pi}{2}+3\text{x})$
$\Rightarrow2\text{n}\pi+2\text{x}=\frac{\pi}{2}+3\text{x}$
$\text{x}=(4\text{m}-1)\frac{\pi}{2},\text{m}\in\text{z}$
or
$\Rightarrow2\text{n}\pi-2\text{x}=\frac{\pi}{2}+3\text{x}$
$\text{x}=(4\text{n}-1)\frac{\pi}{10},\text{n}\in\text{z}$

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