<span>=</span>cos^2a-cos^2/sin^2a : sin^2/cos^2-sin^2a=cos^2-cos^2 +cos^2a : sin^2a-sin^2a+sin^2a=cos^2a/sin^2a;
просто заменяешь и сокращаешь: ctg^2=cos^2/sin^2 и tg^2a=sin^2/cos^2a
1) d=a2–a1=7–2=5
a10=a1+9d=2+9•5=47
2) d=a2–a1=–28+30=2
a28=a1+27d=–30+27•2=24
3) d=a2–a1=8–2=6
Сумму каких? Двух? Пяти? 25?))
S2=2+8=10
S5=(2a1+4d)/2•5=(2•2+4•6)/2•5=70
S25=(2a1+24d)/2•25=(2•2+24•6)/2•25=1850
4) b2=2; q=1/2; n=6
b1=b2:q=2:1/2=4
b6=b1•q^5=4•1/32=1/8
S6=(b6•q–b1)/(q–1)=(1/8•1/2–4)/(1/2–1)
= (-63/16)/(-1/2) = (63•2)/16=63/8=
=7 7/8
5) S7=210; a1=2
S7=(2a1+6d)/2•7=(4+6d)/2•7=
=(2+3d)•7=14+21d
14+21d=210
21d=196
d=196:21=9 1/3
В) -t²-3t+1=0
t²+3t-1=0
t=-3+-√13/2
г)3а²+а=7
а(3а+1)=7
а=7 или 3а+1=7
3а=6
а=2
в)-t²+t+3=0
t²-t-3=0
t=1+-√13/2
г)2а²-а=3
а(2а-1)=3
а=3 или 2а-1=3
2а=2
а=1
Ответ:
Таблица краткой записи и графического изображения.
Task/28751900
-------------------
a) sin3α =... || sinα(3-4sin²α)
sin3α =sin(α +2α) =sinα*cos2α +cosα*sin2α =
sinα*(cos²α - sin²α) +cosα*2sinα*cosα =sinα(3cos²α -sin²α)=sinα(3-4sin²α).
-------------------
b) sinα*cosβ= ( sin(α+β) + ... ) /2 || sin(α - β)
2sinα*cosβ - sin(α+β) =2sinα*cosβ - (sinα*cosβ+cosα*sinβ) =
sinα*cosβ - cosα*sinβ =sin(α - β ).
-------------------
c) ... = - sin(α-β) / sinα*sinβ || ctgα - ctgβ
- sin(α-β) / sinα*sinβ = - (sinα*cosβ - cosα*sinβ) / sinα*sinβ =
cosα*sinβ /sinα*sinβ - sinα*cosβ / sinα*sinβ = ctgα - ctgβ .
-------------------
d) tgα - ctgβ = - cos(α+β) / ... || cosα *sinβ
- cos(α+β) / (tgα -ctgβ) = cos(α+β) / ( cosβ / sinβ - sinα / cosα) =
cos(α+β)*cosα*sinβ / (cosα*cosβ-sinα*sinβ)=cos(α+β) *cosα*sinβ /cos(α+β) = cosα *sinβ .
-------------------
e) cosα +sinα = ... || √2cos(α -π/4).
cosα +sinα =cosα +cos(π/2 - α) =2cos(α +π/2 - α)/2 * cos(α -(π/2 - α )) /2=
2cos(π/4 ) * cos(α -π/4) =√2cos(α -π/4).
или
cosα +sinα =√2( 1/√2)*cosα + (1/√2)*sinα ) =
√2( cos(π/4)*cosα + sin(π/4)*sinα) ) =√2cos(x - π/4) .
-------------------
f) ... = 2sin²(α/2) || 1 - cosα .
2sin²(α/2) =sin²(α/2) + sin²(α/2) = 1 - cos²(α/2) + sin²(α/2) =
1 -( cos²(α/2) - sin²(α/2) ) = 1 cos(2*(α/2) ) = 1 - cosα .
-------------------
g) 1- sinα =2sin² ... || (π/4 -α/2) .
1- sinα =1 - cos(π/2 -α) =1-cos2(π/4-α/2) =1-(cos²(π/4 -α/2)-sin²(π/4-α/2) ) = (1- cos²(π/4 -α/2) )+sin²(π/4-α/2) =sin²(π/4-α/2) +sin²(π/4-α/2) =
2sin²(π/4-α/2) .
* * * * * * * * все можно было написать сразу * * * * * * * *
Удачи !