Evaluate sin20 degrees multiplied by cos20 degrees multiplied by cos40 degrees divided by cos10 degrees Please don't skip the steps,

Evaluate sin20 degrees multiplied by cos20 degrees multiplied by cos40 degrees divided by cos10 degrees Please don't skip the steps,

Sin20 °× cos20 °× cos40 ° / cos10 degree = 1 / 2 × 2sin20 °× cos20 °× cos40 ° / cos10 degree = 1 / 2sin40 °× cos40 ° / cos10 degree = 1 / 2 × 1 / 2 × 2sin40 °× cos40 ° / cos10 degree = 1 / 4sin80 ° / cos10 degree = 1 / 4cos10 ° / cos10 degree = 1 / 4
Three perpendicular theorem
In the cube abcd-a1b1c1d1, e and F are the midpoint of edge Aa1 and CC1, respectively
EF / / AC / / a1c1 is EF ⊥ BD, EF ⊥ b1d1 is EF ⊥ plane bdd1b1
The projection of A1C on ABCD is AC ⊥ BD
The projection of A1C on cdc1d1 is CD1 CD1 ⊥ C1d A1C ⊥ plane bdc1
(1) Connecting AC, we can see that AC is parallel to EF, BD1 is perpendicular to AC, and BB1 is perpendicular to AC, so we can see that EF is perpendicular to plane bdd1b1 (if a line is perpendicular to two intersecting lines on the plane, then this line must be perpendicular to the pinnacle plane)
(2) BD1 is perpendicular to AC and A1A, so BD1 is perpendicular to aa1c of pinnacle, so we can know that BD1 is perpendicular to A1C. Similarly, A1C can be proved to be perpendicular to BC1 or c1d1, as long as one of them is proved again. Then, as shown in the theorem in brackets in the first question, AC1 is perpendicular to bdc1
(1) Connecting AC, we can see that AC is parallel to EF, BD1 is perpendicular to AC, and BB1 is perpendicular to AC, so we can see that EF is perpendicular to plane bdd1b1 (if a line is perpendicular to two intersecting lines on the plane, then this line must be perpendicular to the pinnacle plane)
(2) BD1 is perpendicular to AC and A1A, so BD1 is perpendicular to aa1c of pinnacle, so we can know that BD1 is perpendicular to A1C. Similarly, A1C can be proved to be perpendicular to BC1 or c1d1, as long as one of them is proved again. Then, as shown in the theorem in brackets in the first question, AC1 is perpendicular to bdc1
Parallel theorem
Theorem: if a line outside the plane is parallel to a line in the plane, then the line is parallel to the plane
Please prove (that there is no intersection point between a straight line and a plane) by way of disproportion
hypothesis
There is a straight line L1 out of plane a parallel to a straight line L2 in this plane and has an intersection point a with the plane
Because L1 / / L2
So a is not on L2
L1, L2 determine a plane B
A. L2 determines a plane C
Because a is on L1
So plane B = plane C
And because a, L2 is in plane a
So plane B = plane C = plane a
So L1 is in plane a
This is in contradiction with the conditions
So the hypothesis doesn't hold
So if a line out of the plane is parallel to a line in the plane, the line is parallel to the plane
It is known that in the positive proportion function y = (3m-2) x ^ 2 - / M /, y decreases with the increase of X. what is the analytical expression of this positive proportion function?
The exponent is 1, so 2 - | m | = 1, we get: | m | = 1, M = 1 or - 1
Y decreases with the increase of X, so the coefficient
Why is the negative power of X equal to one part of X
a² × a = a³
Multiplication: exponential addition
a³ ÷ a² = a
Division: power exponent subtraction
a ÷ a = a^(1-1) = a^0 = 1
1 ÷ a = a^(0-1) = a^(-1)
What are the properties of inverse proportion function?
The function y = K / X is called inverse proportional function, where k ≠ 0, where x is an independent variable,
1. When k > 0, the image is in the first quadrant and the third quadrant respectively. In the same quadrant, y decreases with the increase of X; when K0, the function is a decreasing function on x0; K
What is the approximate image of y = x2 / 3 (two-thirds power of y = x)?
A parabola with the opening upward and the vertex of origin (0,0)
I'm very interested
To be accurate. You can do it with CAD.
The definition of inverse proportion function
Inverse scale function
A function of the form y = K / X (k is constant and K ≠ 0) is called an inverse proportional function
The value range of independent variable x is all real numbers that are not equal to 0
The image of inverse scale function is hyperbola
When k ＞ 0, the inverse scale function image passes through one or three quadrants and is a decreasing function
When k ＜ 0, the image of inverse scale function passes through two or four quadrants and is an increasing function