Question

Tg^2(5п+п/3)+ctg^2(3п-п/6)

Answer 1

$\tan {}^{2} (5\pi + \frac{\pi}{3} ) + \cot {}^{2} (3\pi - \frac{\pi}{6} ) = \\ = \tan {}^{2} ( \frac{\pi}{3} ) + \cot {}^{2} ( \frac{\pi}{6} ) = (\sqrt{3}) {}^{2} + \\ + ( \sqrt{3} ) {}^{2} = 3 + 3 = 6$
Примечание:ctg(3π-π/6)=-ctg(π/6),но т.к.
ctg²,то -ctg(π/6)*(-ctg(π/6))=ctg²(π/6)