1) sin⁡(α+β)+sin⁡(α-β) 2) (sin⁡(3π/2+α)+sin⁡(2π+α))/(2 - вопрос №1232226708818 от elzamarg 23.05.2023 13:32

Question

Алгебра: 1) 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-cos⁡4α )=4sin⁡2α

elzamarg · Answer

1) =sinacosb+sinbcosa+sinacosb-sinbcosa=2sinacosb
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