Tg (2 arcsin 2/3) sin (2 arccos 1/4 ctg(1/2arccos (-1/3))

Question

Tg (2 arcsin 2/3)
sin (2 arccos 1/4
ctg(1/2arccos (-1/3))

Answer 1

Ctg(arccos(-1/3))=1/tg(arccos(-1/3))=1/tg(П+argtg(√(1-1/9)/(-1/3)))=1/tg(arctg((√8/9)/(-1/3)))=-√2/4;
sin(2arccos1/4)=2sin(arccos1/4)cos(arccos1/4)=2*1/4*sin(arcsin√(1-1/16))=1/2*√154=√15/8