Sine and cosine theorem? 1. In known △ ABC, cosa = 4 / 5 (A-2): B: (c + 2) = 1:2:3, judge the shape of △ ABC 2, prove that (a ^ 2-B ^ 2-C ^ 2) Tana + (a ^ 2-B ^ 2 + C ^ 2) tanb = 0; cos2a / A ^ 2-cos2b / b ^ 2 = 1 / A ^ 2-1 / b ^ 2

Sine and cosine theorem? 1. In known △ ABC, cosa = 4 / 5 (A-2): B: (c + 2) = 1:2:3, judge the shape of △ ABC 2, prove that (a ^ 2-B ^ 2-C ^ 2) Tana + (a ^ 2-B ^ 2 + C ^ 2) tanb = 0; cos2a / A ^ 2-cos2b / b ^ 2 = 1 / A ^ 2-1 / b ^ 2

1. From (A-2): B: (c + 2) = 1:2:3, let A-2 = t, B = 2T, C + 2 = 3T, (T > 0)
That is: a = t + 2, B = 2T, C = 3t-2
According to the cosine theorem: cosa = (B & # 178; + C & # 178; - A & # 178;) / (2BC)
So: [(2t) & # 178; + (3t-2) & # 178; - (T + 2) & # 178;] / [2 * (2t) * (3t-2)] = 4 / 5
The solution is: T = 4
Then: a = 6, B = 8, C = 10,
There are: A & # 178; + B & # 178; = C & # 178;
So △ ABC is a right triangle, where ∠ C is a right angle
2 (1) from the cosine theorem, 2BC = (B & # 178; + C & # 178; - A & # 178;) / cosa, 2Ac = (A & # 178; + C & # 178; - B & # 178;) / CoSb,
So: (a-178; - b-178; - c-178;) Tana + (a-178; - b-178; + c-178;) tanb
=-(b²+c²-a²)sinA/cosA+(a²+c²-b²)sinB/cosB
=-2bcsinA+2acsinB
=-2(bcsinA-acsinB)
From the formula of triangle area, we get that
S=bcsinA/2=acsinB/2
That is: bcsina acsinb = 0
So: (A & ~ 178; - B & ~ 178; - C & ~ 178;) Tana + (A & ~ 178; - B & ~ 178; + C & ~ 178;) tanb = 0
2(2)cos2A/a²-cos2B/b²
=(1-2sin²A)/a²-(1-2sin²B)/b²
=1/a²-1/b²+2(sin²B/b²-sin²A/a²) （*)
According to the sine theorem: A / Sina = B / SINB, that is: Sin & # 178; a / A & # 178; = Sin & # 178; B / B & # 178;
Then: Sin & # 178; B / B & # 178; - Sin & # 178; a / A & # 178; = 0
Therefore, it can be proved from (*):
cos2A/a²-cos2B/b²=1/a²-1/b²

The usage of verb ing
Be concise and clear

I have a note. I'll type it out for you. It's usually used in the present progressive tense. It's a sensory verb followed by the verb ing (such as saw). I can see that someone is doing something. Some verbs in English can only use (verb ing or noun) as the object. The common ones are: enjoy, finish, mind, feel like

Through the experience after the introduction of the basic principles of Marxism, about 2000 words

Marxist philosophy is a scientific world outlook and methodology. The Sinicization of Marxist philosophy is the innovation and development of Marxist Philosophy in the practice of Chinese revolution, reform and construction, and gives distinct Chinese national form

On the polar coordinate equation
In the polar coordinate equation, given a circle, the center is known (2,3 π), radius is 3, how to find its polar coordinate equation?

To solve the coordinates of the center of a circle x = 2 * 1 / 2 = 1, y = 2 * √ 3 / 2 = √ 3, the center of a circle (1, √ 3), r = 3, the circle is (x-1) &# 178; + (Y - √ 3) &# 178; = 9, then x & # 178; + Y & # 178; - 2 (x + √ 3Y) = 6 and X & # 178; + Y & # 178; = ρ & # 178; X = ρ cos θ y = ρ sin θ, so ρ & # 178; - 2 (ρ C

In the triangle ABC, acosb bcosa = 1 / 2C, Tana = 3tanb is proved

∵aCOSB-bcosA=1/2c
Ψ sinacosb sinbcosa = 1 / 2sinc (using sine theorem)
If a + B + C = π, then C = π - (a + b)
∴sinAcosB-sinBcosA=1/2sin（A+B)
That is, 2sinacosb-2sinbcosa = sinacosb + sinbcosa
sinAcosB=3sinBcosA
∴tanA=3tanB

You_____ can have pairs of sports shoes.
A.each
B.every
C.all
D.everyone

Choose a, each

It is known that the area of triangle ABC is 26 square centimeters and BC is 10 centimeters. What is the distance from point a to line BC?

Ah ~ ~! Children can't go to school. Quadrilateral area = bottom * height. Isn't a triangle half of a quadrilateral? Divide by 2

The greatest common factor of the two numbers is 12, and the least common multiple is 168. One of them is 84, and what is the other number?

The other number is 24

If the corresponding sides of two similar triangles are 3cm and 5cm respectively, and the perimeter of the smaller triangle is 15cm, the perimeter of the larger triangle is 15cm______ cm．

Let the perimeter of the larger triangle be xcm. According to the meaning of the question, we get: 15: x = 3: 5. The solution is x = 25cm

1、 The greatest common divisor of two positive integers is 6 and the least common multiple is 90
How many pairs are there in the first pair of large numbers composed of two positive integers of
1. How to find the greatest common divisor of two numbers
2. How to find the least common multiple of two numbers
3. The first pair of large numbers composed of two positive integers
4. Explain the problem in detail

The greatest common divisor of two integers is 6, and the least common multiple is 90, so 90 / 6 = 15 = 3 * 5, so factors 3 and 5 cannot be shared by integers at the same time. Considering the large number in the front, the large number = 6 * 3 * 5 or 6 * 5 is 90 or 30, and the decimal number is 6 and 6 * 3 = 18, that is, two pairs of numbers (90,6) and (30,18) meet the requirements
I won't explain anything else. You can read by yourself