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Опубликовано 4 года назад по предмету Алгебра от Guilbert

Тригонометрия. Упростите. Cpoчно!

1) (sin^2x - cos^2x)^2 + sin^2*2x

2)((1/1-tgx) - (1/1+tgx))*(cos^2*x)

3) (tg^3*x-tg^3*y)/((1+tgxtgy)(tg^2*x+tgxtgy+tg^2*y))

  1. Ответ
    Ответ дан qnyqiny
    ( sin^{2} x - cos^{2} x)^{2} + sin^{2} 2 x= cos^{2} 2x + sin^{2} 2x= 1
     frac{1}{1-tgx}  -  frac{1}{1+tgx} * cos2x =  frac{1+tgx-1+tgx}{(1-tgx)(1+tgx)} *cos2x =  frac{2 tgx}{1-tg^{2}x} * cos2x = tg2x* cos2x = frac{sin2x * cos2x}{cos2x} = sin2x
     frac{tg^{3} x-tg^{3}y}{(1+tgx tgy)*(tg^{2}+tgx tgy+tg^{2})} =  frac{(tgx-tgy)*(tg^{2}+tgx tgy+tg^{2})}{(1+tgx tgy)*(tg^{2}+tgx tgy+tg^{2})} = frac{(tg x-tg y)}{(1+tg x tg y)} = tg (x-y)