Представить в виде произведения сумму:

a) tg4π/5-tg3π/4

b) ctg2x-tg4x

c) tg5π/8-ctgπ/8

d) tg5x+ctg8x

A) tg4π/5-tg3π/4 = sin (4π/5 - 3π/4) / cos4π/5*cos3π/4 = sin (π/20) / cos4π/5*cos3π/4;

b) ctg2x-tg4x = tg (π/2-2x) - tq4x = sin (π/2-2x - 4x) / cos (π/2-2x) * cos4x = = cos6x / (sin2x*cos4x) ;

c) tg5π/8-ctgπ/8 = tg5π/8-tg (π/2 - π/8) =

=sin (5π/8 - (π/2 - π/8)) / (cos5π/8*cos (π/2 - π/8)) = - cos3π/8 / (cos5π/8*sinπ/8) ;

d) tg5x+ctg8x = tq5x + tq (π/2 - 8x) = sin (5x + π/2 - 8x) / (cos5x * cos (π/2 - 8x)) =

=sin (π/2 - 3x) / (cos5x * sin 8x)) = cos3x / (cos5x * sin 8x)).