Double angle formula of cosine

Double angle formula of cosine

Double angle formula
sin2α=2sinαcosα,
cos2α=cos2α-sin2α=2cos2-1=1-2sin2α
There are two variants as follows:
sin2α=sin2α+π4-cos2α+4π=2sin2a+4π-1=1-2cos2α+4π;
cos2α=2sinα+4πcosα+4π

If vector a=（1，λ，2）， b=（2，-1，2）. a， The cosine of the angle B is 8 9, then the value of λ is () A. 2 B. -2 C. -3 D. 3

Set vector
a，
If the angle of B is θ, then
∵ vector
a=（1，λ，2），
b=（2，-1，2），
∴cosθ=2-λ+4
1+λ2+4•
4+1+4=6-λ
Three
5+λ2=8
9，
The solution is λ = - 2,
Therefore, B

If the vector a and B satisfy (a-b) (2a + b) = - 4, and a = 2, B = 4, then the cosine value of the angle between vector a and B is?

Let the angle between vector a and vector b be θ,
(a-b)(2a+b)=-4,
2a^2-2ab+ab-b^2=-4
2(|a|^2)-ab-|b|^2=-4
2*4-ab-16=-4
ab=-4=|a|*|b|*cosθ=8cosθ
Cos θ = - 0.5
We get θ = 120 degrees

How did the deformation formula of double angle cosine come from

Cos 2A = cos 2a-sin? A = (1-sin? A) - sin? A = 1-2sin? Acos2a = cos? A-SiN? A = cos? A - (1-cos? A) = 2cos? A-1cos2a = 1-2sin? A. sin? A = (1-cos2a) / 2cos2a = 2cos? A-1 is obtained

2. Cosine formula of angle difference 1. Given that α and β are acute angles, cos α = 4 / 5, sin (α - β) = - √ 10 / 10, find cos β 2. The value of COS 43 ° sin 77 ° to sin 43 ° sin 167 ° is The more detailed the better. If I can understand, there are extra points

1. Cos β = cos [α - (α - β)] = cos α cos (α - β) + sin α sin (α - β) = 4 / 5 * (3 / 10) + 3 / 5 * (- √ 10 / 10) = (12-3 √ 10) / 502

Senior one mathematics collection. Compulsory 1 of Beijing Normal University Let a = {x | (x-1) (x + 2) (x-3) = 0}, B = {x | - 1 ＜ 2x + 1 ≤ 3}, C = {x | 3x-1 ≥ 2} Ask for an expert to answer

Simplification: a = {- 2,1,3}
B={X|-1＜X≤1}
C={X|X≥1}
（A∪B）∩C
=（A∩C）∪（B∩C）
={1,3}∪{1}
={1,3}

Answers to the questions after class 1 of Mathematics for senior one in Beijing Normal University

Ah, all reference books have answers. Just buy one by yourself

Compulsory course 2) 1. Given that the generatrix length of the cylinder is 6 cm and the radius of its bottom surface is 2 cm, the axial sectional area of the cylinder is calculated 2. It is known that the bus length of the cone is 10 cm, the angle between the generatrix and the axis is 30 ·, and the radius of the upper and lower bottom surface is 5cm

1. The axial sectional area of the cylinder = ground diameter × cylinder height = 2 × 2 × 6 = 24 square centimeter
2. Bottom radius = 5 + 10sin30 = 5 + 5 = 10cm
Bottom area = π 10 ^ 2 = 100 π cm2

Summer homework fifth grade mathematics Beijing Normal University Edition 1. A cuboid fish tank with a length of 2 decimeters and a width of 1.8 decimeters. After a goldfish is put in, the water surface rises by 0.3 decimeters. What is the volume of this fish? 2. A swimming pool is 50 meters long and 25 meters wide. It is full of 2500 cubic meters of water (1) What is the depth of the swimming pool? (2) If you want to paste ceramic tiles in the swimming pool, how many tiles need the following specifications? The side length is: 5 decimeter × 5 decimeter square brick 3. After the ice turns into water, the volume will be reduced by one eleventh. The volume of a piece of ice after being turned into water is 4 cubic meters. How many cubic centimeters is the original volume of this piece of ice? Good hearted person, help me, only these questions! Or I'll be miserable! Help! Thank you very much! More details, thank you!

1.2*1.8*0.3=1.08
Two
1.2500/(25*50)=2
2.25*50+50*2*2+25*2*2=1550
1550 / (5 * 5) = 62 pieces

Excuse me, who has the unit test questions of the first and second volumes of primary school mathematics of Beijing Normal University Edition, can you give me one?

4.35 × 1.02 ﹤ 4.353.98 ﹤ 1.2 ﹤ 3.980.98 × 0.98 ﹤ 0.98 40.5 ﹥ 0.8 ﹤ 0.8 ﹤ 40.58.24 × 10 8.243.9 ﹤ 0.99 ﹤ 3.910, 0.25 × 9.7 × 4 = 9.7 × (×) 2. Judgment (every 1 point, 6 points in total) 1