Verified answer

Объяснение:

1.

arccos√3/2+arctg(tg4π/7)+

+arcctg(ctg(-π/4))=kπ

π/6+arctg(-tg(3π/7))+arcctg(ctg(7π/4))=πk

π/6-arctg(tg(3π/7))+arcctg(-ctg(π/4))=πk

π/6-3π/7+π-arcctg(ctg(π/4))=πk

π/6-3π/7+π-π/4=πk

14π/84-36π/84+84π/84-21π/84=πk

41π/84=πk

84πk=41π

k=41/84

ответ: k=41/84

2.

8arccos²x+2πarccosx-π²=0 ; x∈[-1;1]

arccos=t

8t²+2πt-π²=0

D=(2π)²-4×8×(-π²)=4π²+32π²=36π²

t1=(-2π+6π)/16=π/4

t2=(-2π-6π)/16= -π/2

arccosx=π/4 ; x=cosπ/4=√2/2

arccosx= -π/2 ; ø ,т.к х∈[0;π]

ответ: √2/2