Question

ЛЕГКИЙ ВОПРОС!!!
вычислите tg8x если tg2x=1/4

Answer 1

$tan8x=frac{2tan4x}{1-tan^24x}\tan4x=frac{2tan2x}{1-tan^22x}=frac{2*frac{1}{4}}{1-(frac{1}{4})^2}=frac{frac{1}{2}}{frac{15}{16}}=frac{8}{15}\tan8x=frac{2*frac{8}{15}}{1-(frac{8}{15})^2}=frac{frac{16}{15}}{frac{161}{225}}=frac{240}{161}$