1) (cos5α+cos6α+cos7α) / (sin5α+sin6α+sin7α);

2) tg (45˚+3α) - tg (45˚-3α).

1

Воспользуемся формулами

cosa+cosb=2cos (a+b) / 2*cos (a-b) / 2

sina+sinb=2sin (a+b) / 2*cos (a-b) / 2

(2cos6acosa+cos6a) / (2sin6acosa+sin6a) = cos6a (2cosa+1) / [sin6a (2cosa+1) ]=

=ctg6a

2

Воспользуемся формулами

tg (a+b) = (tga+tgb) / (1-tgatgb)

tg (a-b) = (tga-tgb) / (1+tgatgb)

(tg45+tg3a) / (1-tg45tg3a) - (tg45-tg3a) / (1+tg45tg3a) =

(1+tg3a) / (1-tg3a) - (1-tg3a) / (1+tg3a) = [ (1+tg3a) ² - (1-tg3a) ²] / (1-tg²3a) =

= (1+tg3a-1+tg3a) (1+tg3a+1-tg3a) / (1-tg²3a) = 4tg3a / (1-tg²3a) = 2tg6a