Solve the trigonometric equation 8-(5x+2)=-5x-6

 Exercise

$\frac{1}{3}\cot\left(2x\right)=1$

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Multiply both sides of the equation by $3$

$\cot\left(2x\right)=3$

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Take the inverse of $\cot\left(2x\right)$ on both sides

$\mathrm{arccot}\left(\cot\left(2x\right)\right)=\mathrm{arccot}\left(3\right)$

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Apply the formula: $\mathrm{arccot}\left(\cot\left(\theta \right)\right)$$=\theta $, where $x=2x$

$2x=\mathrm{arccot}\left(3\right)$

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Divide both sides of the equation by $2$

$x=\frac{\mathrm{arccot}\left(3\right)}{2}$

$x=\frac{\mathrm{arccot}\left(3\right)}{2}$

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