Question

Question :


Find the value of ➡

$\sf \: {cot}^{2} \: \dfrac{\pi}{7} + {cot}^{2} \: \dfrac{2\pi}{7} + {cot}^{2} \: \dfrac{3\pi}{7}$
​

Answer 1

Answer:

5.47

Step-by-step explanation:

$\implies \sf \: {cot}^{2} \: \dfrac{\pi}{7} + {cot}^{2} \: \dfrac{2\pi}{7} + {cot}^{2} \: \dfrac{3\pi}{7}$

For easy calculation, put the values in the brackets for solving.

$\implies \sf \: cot^2 \bigg(\dfrac{\pi}{7} \bigg) + cot^2 \bigg(\dfrac{2 \pi}{7} \bigg) + cot^2 \bigg( \dfrac{3 \pi}{7} \bigg)$

Converting the π value in the degree.

We get,

$\implies \sf \pi = 180^{\circ}$

$\implies \sf cot^2 (25.714) + cot^2 (51.429) + cot^2 (77.142)$

$\implies \sf (2.1742)^2 + (0.8273)^2 + (0.2475)^2$

$\implies \sf 4.731 + 0.68 + 0.06$

$\implies \bf 5.47$

$\therefore \bf The \: value \: of \: {cot}^{2} \: \dfrac{\pi}{7} + {cot}^{2} \: \dfrac{2\pi}{7} + \\ \sf {cot}^{2} \: \dfrac{3\pi}{7} \: is \: 5.47.$

Answer 2

$\implies \sf \: {cot}^{2} \: \dfrac{\pi}{7} + {cot}^{2} \: \dfrac{2\pi}{7} + {cot}^{2} \: \dfrac{3\pi}{7}$

For easy calculation, put the values in the brackets for solving.

$\implies \sf \: cot^2 \bigg(\dfrac{\pi}{7} \bigg) + cot^2 \bigg(\dfrac{2 \pi}{7} \bigg) + cot^2 \bigg( \dfrac{3 \pi}{7} \bigg)$

Converting the π value in the degree.

We get,

$\implies \sf \pi = 180^{\circ}$

$\implies \sf cot^2 (25.714) + cot^2 (51.429) + cot^2 (77.142)$

$\implies \sf (2.1742)^2 + (0.8273)^2 + (0.2475)^2$

$\begin{gathered} \\ \end{gathered}$

$\implies \sf 4.731 + 0.68 + 0.06$

$\implies \bf 5.47$

$\begin{gathered}\therefore \bf The \: value \: of \: {cot}^{2} \: \dfrac{\pi}{7} + {cot}^{2} \: \dfrac{2\pi}{7} + \\ \sf {cot}^{2} \: \dfrac{3\pi}{7} \: is \: 5.47.\end{gathered}$

☘Hope it helps❢❢

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Glad to help u

❀Thankew❀