Question

Вычислите:
1) 1-tgПи/6+tg^2Пи/6-tg^3Пи/6
2) 1+cosПи/6+ cos^2Пи/6+cos^3Пи/6

Answer 1

1) $1- frac{1}{ sqrt{3}} + frac{1}{3}- frac{1}{3 sqrt{3}} = frac{4}{3}- frac{4}{3 sqrt{3} }= frac{4}{3}(1- frac{1}{ sqrt{3} } )= frac{4( sqrt{3}-1)}{3 sqrt{3} }$
2) $1+ frac{ sqrt{3}}{2}+ frac{3}{4}+ frac{3 sqrt{3}}{8}= frac{8+4 sqrt{3}+6+3 sqrt{3}}{8}= frac{14+7 sqrt{3} }{8} = frac{7(2+ sqrt{3})}{8}$