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Exercise

$\sqrt{3}\cot\left(\frac{5\pi}{7}\right)x=3$

Step-by-step Solution

1

Divide both sides of the equation by $\sqrt{3}$

$\cot\left(\frac{5\pi }{7}\right)x=\frac{3}{\sqrt{3}}$
2

Divide both sides of the equation by $\cot\left(\frac{5\pi }{7}\right)$

$x=\frac{3}{\cot\left(\frac{5\pi }{7}\right)\sqrt{3}}$

Verify that the solutions obtained are valid in the initial equation

3

The valid solutions to the equation are the ones that, when replaced in the original equation, don't result in any square root of a negative number and make both sides of the equation equal to each other

$x=\frac{3}{\cot\left(\frac{5\pi }{7}\right)\sqrt{3}}$

Final answer to the exercise

$x=\frac{3}{\cot\left(\frac{5\pi }{7}\right)\sqrt{3}}$

Try other ways to solve this exercise

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