It is known that Tan θ + sin θ = a, Tan θ - sin θ = B, and proved that: (A2-B2) 2 = 16ab

It is known that Tan θ + sin θ = a, Tan θ - sin θ = B, and proved that: (A2-B2) 2 = 16ab

It is proved that: ∵ (A2-B2) 2 = [(a + b) (a-b)] 2 = [(Tan θ + sin θ + Tan θ - sin θ) (Tan θ + sin θ - Tan θ + sin θ)] 2 = 16tan 2 θ sin 2 θ, and 16ab = 16 (Tan 2 θ - Sin 2 θ) = 16 · sin 2 θ sin 2 θ Cos2 θ = 16 · Tan 2 θ sin 2 θ. Therefore, (A2-B2) 2 = 16ab

How to use English to say the differential of SiNx, how to use English to say the integral of SiNx,

Differentiate for sinx
Integrals of sinx

In the cube abcd-a1b1c1d1 with edge length a, m and N are the midpoint of Aa1 and c1d1 respectively. If the plane passing through DMN and the line A1B1 intersect at P, then the length of line PB1 is?
The answer is 3 / 4P. Why is point P in that position?

First, determine the position of point P. extend DM and intersect d1a1 with E. connect en and intersect A1B1 with P
Because: e, n are both on the plane DMN, and on the plane a1b1c1d1
So en is the intersection of the two planes. The intersection P of en and A1B1 is the intersection of line A1B1 and plane DMN
Let's find the length of PB1
In the triangle dd1e, a1m / / d1d, and a1m = (1 / 2) d1d,
That is: d1a1 = a1e, that is, MA1 is the median line
Thus, we know that a1p is the median line in the triangle d1en, and a1p = (1 / 2) d1n = (1 / 4) a
Thus: PB1 = A1B1 - a1p = (3 / 4) a

The third power of 1 = the second power of 1, the third power of 1 + the third power of 2 = the second power of 3, the third power of 1 + the third power of 2 + the third power of 3 = 6 square, find the law and express it with the equation

1^3+2^3+…… n^3=(1+2+…… +n)^2

Given the set a = {x | X & sup2; + (M + Z) x + 1 = 0}, B {x | x > 0} if a ∩ B = & # 8709; find the value range of M

1. A is an empty set
That is, (M + Z) ^ 2-4 = 0
-(m+z)0
Another range of M is solved, and the last two ranges are union set

X / (x2 + 5x + 1) = 4, X2 / (x4-5x2 + 1) =? (please note that the number after X is power.)

x=4(x²+5x+1)=4x²+20x+4
4x²+4=-19x
Square on both sides
16x^4+32x²+16=361x²
Subtract 112x and 178 from both sides;
16x^4-80x²+16=249x²
16(x^4-5x²+1)=249x²
x²/(x^4-5x²+1)=16/249

In △ ABC, ab = 8, BC = 5, CA = 6. How many parallelograms can be drawn with two sides as sides and the other side as diagonals?

A parallelogram can be drawn by taking one side as a diagonal,
The triangle has three sides and three parallelograms can be drawn

40% x-3 / 8 = 5 / 12

0.4x-3/8=5/12
0.4x=10/24+9/24
x=19/24 *10/4
x=95/48

The tangent equation of the curve y = x / (2 + x) at the point (- 1, - 1) is
The tangent equation of the curve y = x / (2 + x) at the point (- 1, - 1) is

The tangent point is (- 1, - 1)
y=x/(2＋x)
Then:
y'=[(x)'(2＋x)－x(2＋x)']/(2＋x)²
y'=2/(2＋x)²
Then the tangent slope is k = y '| (x = - 1) = 2
The tangent equation is:
y=2(x＋1)－1
The results are as follows
2x－y＋1=0

In rational numbers, are there the largest positive number and the smallest negative number? Are there the largest negative integer and the smallest positive integer? If so, what are the numbers?

There is no maximum positive number and minimum negative number
There are the largest negative integer - 1 and the smallest positive integer 1