If (x + \( \frac{1}{x} \)) = k, find the value of x³ + \( \frac{1}{x^3} \)
Find the value of \(\frac{\sin^{2}10^{\circ}+\sin^{2}20^{\circ}+\sin^{2}30^{\circ}+\sin^{2}40^{\circ}+\sin^{2}50^{\circ}+\sin^{2}60^{\circ}+\sin^{2}70^{\circ}+\sin^{2}80^{\circ}+\sin^{2}90^{\circ}}{\cos^{2}20^{\circ}+\cos^{2}40^{\circ}+\cos^{2}50^{\circ}+\cos^{2}70^{\circ}+\cot^{2}45^{\circ}}\) is:
\( \frac{3}{4} \)
\( \frac{5}{3} \)
\( \frac{6}{5} \)
\( \frac{4}{3} \)