Question
Find the general solutions of the following equations: $\sin2\text{x}+\cos\text{x}=0$
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Answer
We have, $\sin2\text{x}+\cos\text{x}=0$ $2\sin\text{x}\cos\text{x}+\cos\text{x}=0$ $\cos\text{x}\text{(2sinx+1)}=0$ $\cos\text{x}=0$ or $2\sin\text{x+1}=0$ $\text{x}=\text{(4m}-1)\frac{\pi}{2}$ or $\sin\text{x}=\frac{-1}{2}$ $\text{x}=\text{(4m}-1)\frac{\pi}{2}$ or $\text{x}=\text{(4n}-1)\frac{\pi}{6},\text{m,n}\in\text{z}$
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