1)упростите sin⁡(α+β)+sin⁡(α-β) 2) (sin⁡(3π/2+α)+sin⁡(2π+α))/(2 cos⁡(-α) sin⁡(-α)+1)...

Question

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-cos⁡4α )=4sin⁡2α

Answer 1

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