Why arctan (1 / x) = arccot (x) No wealth to give... Help me···

Why arctan (1 / x) = arccot (x) No wealth to give... Help me···

Because (arctan (1 / x)) '= - 1 / (1 + x ^ 2), (arccot (x))' = - 1 / (1 + x ^ 2)
So arctan (1 / x) = arccot (x)

Why is arctan (e ^ x) + arctan (e ^ - x) equal to half π?

arctan（e^x）+arctan（e^-x）
＝arctan（e^x）+arctan（1/e^x）
=arctan（e^x）+arccot（e^x）
=π/2

A and B vehicles leave from two places at the same time. When they meet 18 kilometers away from the midpoint, the speed ratio of a and B vehicles is 7:6. What's the distance between a and B

18 × 2 ÷ (7-6) × (7 + 6) = 36 × 13 = 468km

If the area of a rectangle is the root sign 3 and one side of it is 3 - √ 3, what is the length of the other side

Radical 3 / (3-radical 3)

In the triangle ABC, a + B + C = 90, and a = 40, find the area of the triangle ABC

a=40
b+c=50
a²=b²+c²-2bccosA
=(b+c)²-2bc-2bccosA
40²=50²-2bc(1+cosA)
bc(1+cosA)=900
S=bcsinA/2=900sinA/2(1+cosA)=450sinA/(1+cosA)=
Let's go on

Ask a physics application question of junior three, about the lever
The mass of a wooden stick with uniform thickness is 50kg. When one end of the stick is on the ground, how much force does it need to lift the other end? (G is 10N / kg)
Which expert will Please help me

50*10/2=250N

Use a 16 decimeter long wire to form a circle. The joint is 0.3 decimeter long. What is the area of the circle?

(16-0.3) △ 3.14 △ 2 = 2.5 (decimeter), 3.14 × 2.52, = 3.14 × 6.25, = 19.625 (square decimeter); answer: the area of this circle is 19.625 square decimeter

Prove that integers larger than 11 can be decomposed into the sum of two composite numbers

If this number a is even, it can be divided into 4 and A-4. Because a11, even numbers with a-47 greater than 2 are composite numbers, and 4 is composite numbers, so it can be divided into two composite numbers
2. If this number a is odd, it can be divided into 9 and A-9. Because a11, even numbers with a-94 greater than 2 are composite numbers, and 9 is composite numbers, it can be divided into two composite numbers

Primary school mathematics grade 6 Volume 1 questions
A. B two cars leave from two cities at the same time and go opposite each other. A car travels 75 kilometers per hour, B car travels 85 kilometers per hour. The two cars meet at 20 kilometers away from the midpoint. How many kilometers is the distance between the two cities? 1 thank you!

40 (85-75) = 4 (hours) they drove for four hours
(85 + 75) * 4 = 640 (km)
A: the two cities are 640 kilometers apart
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Besides, it's wrong to mention that car B has traveled 20 + 20 kilometers more than car a, not 20 kilometers

If the height of a 5 cm cylinder increases by 3 cm, its surface area will increase by 18.84 square cm. What is the volume of the original cylinder?

The circumference of the bottom surface of the original cylinder is: 18.84 △ 3 = 6.28 (CM), the radius of the bottom surface of the original cylinder is: 6.28 △ 3.14 △ 2 = 1 (CM), the volume of the original cylinder is: 3.14 × 12 × 5 = 15.7 (cm3), a: the volume of the original cylinder is 15.7 cm3