Solve the following equations: 4 +2 +2 +1=0 - Vidyadip

Question

Solve the following equations: $4\sin\text{x}\cos\text{x}+2\sin\text{x}+2\cos\text{x}+1=0$

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Answer

$4\sin\text{x}\cos\text{x}+2\sin\text{x}+2\cos\text{x}+1=0$ $\Rightarrow2\sin\text{x}(2\cos\text{x}+1)+1(2\cos\text{x}+1)=0$ $\Rightarrow(2\sin\text{x}+1)(2\cos\text{x+1})=0$ $\Rightarrow2\sin\text{x}+1=0$ or $2\cos\text{x}=-\frac{1}{2}$ $\Rightarrow\sin\text{x}=\sin\frac{7\pi}{6}$ or $\cos\text{x}=\frac{2\pi}{3}$ $\Rightarrow\text{x}=\text{n}\pi+(-1)^\text{n}\frac{7\pi}{6}$ or $\text{x}=2\text{n}\pi\pm\frac{2\pi}{3},\text{n}\in\text{Z}$

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