Untitled

b
2=π 2−a+c 2
sin b
2= cos a+c 2
2dmb = 4 cos a
2hcos a 2cos c 2−sin a 2sin c 2icos c 2
= 4 cos2a
2cos2c 2−4 sin a 2cos a 2sin c 2cos c 2
= (1 + cos a)(1 + cos c)−sin asin c
= 1 + cos a+ cos c+ cos acos c−sin asin c
= 1 + cos a+ cos c+ cos(a+c)
cos(a+c) = −cos b
ADC
AD =AC sin ˆ C
ABC
AC
sin ˆ B=BC sin ˆ A
AD =BC sin ˆ
Bsin ˆ C
sin ˆ A
ˆ
A= 180◦−(ˆ B+ˆ C) = 180◦−70◦−84◦= 26◦
AD = 1750sin(70◦) sin(84◦)
sin(26◦)= 3731m

AH =a−b
2
tg ˆ A=h
AH =2h a−b,ˆ
A < π
2
ˆ
A+ˆ D=πˆ D=π−ˆ A
`=h
sin ˆ A
ABD
2R=BD
sin ˆ A
BD
BD2=a2+`2−2a` cos ˆ A
a= 100, b = 80, h = 50
tg ˆ A=2·50
100 −80 = 5
ˆ
A= 1,3734rad
ˆ
C= 1,7682
sin ˆ A= 0,9806
`=50
sin ˆ A= 50,9902
BD =qa2+`2−2a` cos ˆ A= 102,9563
R= = BD
2 sin ˆ A= 52,4976
I
I= sin3xsin π
2−3x+ cos3xcos π 2−3x= sin3xcos 3x+ cos3xsin 3x
sin 3xcos 3x

cos 3x= cos(2x+x)
= cos 2xcos x−sin 2xsin x
= (2 cos2−1) cos x−2 sin2xcos x
= 2 cos3x−cos x−2 cos x+ 2 cos3x
= 4 cos3x−3 cos x
cos3x=1
4(cos 3x+ 3 cos x)
sin 3x= sin(2x+x)
= sin 2xcos x+ sin xcos 2x
= 2 sin xcos2x+ sin x(1 −2 sin2x)
= 2 sin x(1 −sin2x) + sin x−2 sinx
= 3 sin x−4 sin3x
sin3x=1
4(3 sin x−sin 3x)
I
I=3
4sin xcos 3x−1 4sin 3xcos 3x+1 4cos 3xsin 3x+3 4cos xsin 3x
=3
4(sin xcos 3x+ cos xsin 3x)
=3
4sin 4x
3
4sin 4x≥3√3 8
sin 4x≥√3
2
4x∈[π
3,2π 3] 2π
π
3+ 2kπ ≤4x≤2π 3+ 2kπ
π
12 +kπ 2≤x≤π 6+kπ 2