Question

Представить в виде произведения сумму:

a)tg4π/5-tg3π/4
b)ctg2x-tg4x
c)tg5π/8-ctgπ/8
d)tg5x+ctg8x

Answer 1

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)) .