Разность прогрессии:
d = a₂ - a₁ = 5,6 - 5 = 0,6
Пятый член:
а₅ = а₁ + 4d = 5 + 4*0,6 = 5 + 2,4 = 7,4
Сумма 10 первых членов:
![\tt S_{10}=\cfrac{2a_1+d(n-1)}{2}\cdot n= \cfrac{2\cdot5+0.6(10-1)}{2}\cdot 10=77](https://tex.z-dn.net/?f=%5Ctt%20S_%7B10%7D%3D%5Ccfrac%7B2a_1%2Bd%28n-1%29%7D%7B2%7D%5Ccdot%20n%3D%20%5Ccfrac%7B2%5Ccdot5%2B0.6%2810-1%29%7D%7B2%7D%5Ccdot%2010%3D77)
![\frac{21sin1130cos1130}{sin2260}= \frac{10,5*2sin1130cos1130}{sin2260}= \frac{11sin2(1130)}{sin2260}= \frac{11sin2260}{sin2260}=10,5](https://tex.z-dn.net/?f=+%5Cfrac%7B21sin1130cos1130%7D%7Bsin2260%7D%3D+%5Cfrac%7B10%2C5%2A2sin1130cos1130%7D%7Bsin2260%7D%3D+%5Cfrac%7B11sin2%281130%29%7D%7Bsin2260%7D%3D+%5Cfrac%7B11sin2260%7D%7Bsin2260%7D%3D10%2C5+)
за место десятичной дроби 10,5 можно записать смешанную дробь 10 1/2 или неправильную дробь 21/2
1) т.к. 1.5π<α<2π
то cosα>0
⇒cosα = √(1-sin²α) = √(1-9/25) = 4/5
2)sin(π-α)=sinα
sin(π-α)=sinπ*cosα - sinα*cosπ = [т.к. sinπ=0 и cosπ=-1] = sinπ
3) sin(11π/4) = sin(3π/4) = √2/2
cos(13π/4) = cos(π/4) = √2/2
sin(-2.5π) = sin(-0.5π) = sin(-π/2) = -1
cos(-25π/3) = cos(25π/3) = cos(π/3) = 1/2
(√2/2 - √2/2) *(-1) * (1/2) = 0
4) cosα=-2/3
sinα = ±√(1-cos²α) = ±√(1-4/9) = ±√5/3
⇒|sinα|<1
√((1-sinα)/(1+sinα))=√((1-sinα)²/(1-sin²α))=√((1-sinα)²/cos²α)=|(1-sinα)|/|cosα|
√((1+sinα)/(1-sinα))=√((1+sinα)²/(1-sin²α))=√((1+sinα)²/cos²α)=
=|(1+sinα)|/|cosα|
|(1-sinα)|/|cosα| + |(1+sinα)|/|cosα| = (|1-sinα|+|1+sinα|)/|cosα| =
=(1-sinα+1+sinα)/|cosα| = 2/|cosα| = 2/ (2/3) = 3