1)упростите
sin(α+β)+sin(α-β)
2) (sin(3π/2+α)+sin(2π+α))/(2 cos(-α) sin(-α)+1)
3)Доказать тождество:
(tg α+ctg α)(1-cos4α )=4sin2α
sin(α+β)+sin(α-β)
2) (sin(3π/2+α)+sin(2π+α))/(2 cos(-α) sin(-α)+1)
3)Доказать тождество:
(tg α+ctg α)(1-cos4α )=4sin2α
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Answers & Comments
2) =-cosa+sina /-2sinacosa+sin²a+cos²a=sina-cosa /(sina-cosa)²=
=1 / sina-cosa
3) (sina/cosa +cosa/sina ) (sin²2a+cos²2a-cos²2a+sin²2a) =
=sin²a+cos²a)/sinacosa *2sin²2a=1/sinacosa *8sin²acos²a=8sinacosa=
=4*2sinacosa=4sin2a
тождество верно