971. a)
1
–
1
1 + ctgα 1 − ctgα
=
1 − ctgα − 1 − ctgα 1 − ctg 2 α
=–
2 ctgα 1 − ctg 2 α
=
2 2 tg 2 α − 1 2 tgα tgα =– : = =tg2α. = 2 1 tgα tg α 1 − tg 2 α 1− 2 tg α −
1 − tg α
1−
б)
=
sin 2 α
2 2 2 2 cos 2 α = cos α − sin α : cos α + sin α = sin 2 α 1 + tg 2 α cos 2 α cos 2 α 1+ cos 2 α (cos 2 α − sin 2 α ) cos 2 α 2 2 cos 2 α ⋅ (cos 2 α + sin 2 α ) cos α − sin α 2
=
=
=cos2α
1
sin 2 (45o + α ) − cos 2 (45o + α ) sin 2 (45° + α ) − 1 tg 2 ( 45° + α ) − 1 cos 2 (45° + α ) cos 2 (45o + α ) = в) = = 2 o 2 2 tg ( 45° + α ) + 1 sin (45° + α ) sin (45 + α ) + cos 2 (45o + α ) +1 cos 2 (45o + α ) cos 2 (45° + α )
=
(sin 2 (45° + α ) − cos 2 (45° + α )) cos 2 (45° + α ) = –cos(90°+2α)=sin2α. (sin 2 (45° + α ) + cos 2 (45° + α )) cos 2 (45° + α ) г) (tg2α–2tgα)⋅(ctgα–tgα)=
hochy5.ru (
2 tgα
− 2 tgα )⋅(ctgα–tgα)=
1 − tg 2 α 2 tg 3 α ⋅ ctgα − 2 tg 4 α
=
д)
1 − tg 2 α
tgα
tg 2 α − tgα
=
sin α
cos α
= :
( 2 tgα − 2 tgα + 2 tg 3 α ) ⋅ ( ctgα − tgα )
2 tg 2 α − 2 tg 4 α 1 − tg 2 α 1
sin 2 α
−
sin α
=
1 − tg 2 α 2 tg 2 α (1 − tg 2 α ) 1 − tg 2 α
=
cos 2 α cos α 1 sin α 1 ⋅ = = cos α sin 2α cos α − sin α cos 2α cos 2α ⋅ cos α cos α cos 2α sin α ⋅ cos 2 α sin α = = = cos 2α ; ⋅ cos α sin 2α cos α − sin α cos 2 α sin α
322
=
=2tg2 α.