Solve the following equations: (3-1) +(3+1) =2

Question

Solve the following equations:
$(\sqrt{3}-1)\cos\text{x}+(\sqrt{3}+1)\sin\text{x}=2$

✓

Answer

We have,
$(\sqrt{3}-1)\cos\text{x}+(\sqrt{3}+1)\sin\text{x}=2$
Divide on both side by $2\sqrt{2}$
$\frac{(\sqrt{3}-1)}{2\sqrt{2}}\cos\text{x}+\frac{(\sqrt{3}+1)}{2\sqrt{2}}\sin\text{x}=\frac{1}{\sqrt{2}}$
$\sin\Big(\text{x}+\tan^{-1}\Big(\frac{\sqrt{3}-1}{\sqrt{3}+1}\Big)\Big)=\sin\frac{\pi}{4}$
$\text{x}=2\text{n}\pi+\frac{\pi}{3}$ or $2\text{n}\pi-\frac{\pi}{6}\text{n}\in\text{z}$

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