1. AB, CD are two different-plane lines, then AC, BD must be different-plane lines? 2. Are the two lines c, d intersected with the two lines a, b? 3. There are countless planes parallel to the straight line beyond the straight line. Please state your reasons, 1. AB, CD are two opposite-plane lines, then AC, BD must be opposite-plane lines? 2. Are the two lines c, d intersected with each other respectively? 3. There are countless planes parallel to the straight line beyond the straight line. Please state your reasons,

1. AB, CD are two different-plane lines, then AC, BD must be different-plane lines? 2. Are the two lines c, d intersected with the two lines a, b? 3. There are countless planes parallel to the straight line beyond the straight line. Please state your reasons, 1. AB, CD are two opposite-plane lines, then AC, BD must be opposite-plane lines? 2. Are the two lines c, d intersected with each other respectively? 3. There are countless planes parallel to the straight line beyond the straight line. Please state your reasons,

1. Must be, inverse proof method: Suppose AC, BD may be the same plane straight line, then A, B, C, D four points are on the same plane, then AB, CD are two same plane straight lines, conflict with the conditions, so AC, BD can not be the same plane straight line.2. Let the intersection points of c, d and a, b be A, B, C, D, refer to the first proof method, then c, d must be different.3. Yes, there seems to be this.

F (x)=-2cos [(7π/2)-2x] is an odd function.

Correct.
2 Cos [(7π/2)-2x ]=2 cos (4π-π/2-2x)
=2 Cos [-(2x /2)]
=2 Cos (2x /2)
=-2Sin 2x
So odd function

Correct.
2 Cos [(7π/2)-2x ]=2 cos (4π-π/2-2x)
=2 Cos [-(2x /2)]
=2 Cos (2x /2)
=-2Sin 2x
So it's a singular function.

A Mathematics Judgment Problem of Senior One If a strip is parallel to one of two parallel planes, it is also parallel to the other. Is there anything wrong with this sentence? Just a counterexample! Thank you first!

Wrong. If this line is on another plane, it's not parallel to that plane.

On the Judgment of Sets in Senior One Mathematics Let A=『a, b, c』 If the set M= x|x belongs to A, then A is a subset of M If M =『x|x belongs to A』, the set M has 8 elements Judge its correctness and error and give reasons The Judgment Problem of Set in Senior One Mathematics Let A=『a, b, c』 If the set M= x|x belongs to A, then A is a subset of M If M =『x|x belongs to A』, the set M has 8 elements Judge its correctness and error and give reasons

M=[ x|x belongs to A], which means that the element in M is the element in A, then M=A={ a, b, c}
So, A is the right subset of M, and M has eight element errors
Note: M=『x|x belongs to A』 means that M=A instead of M∈A,
Just as R is a set of real numbers,{ x|x∈R} also represents a set of real numbers.

M=[ x|x belongs to A], which means that the element in M is the element in A, then M=A={ a, b, c}
So, A is the right subset of M, and M has eight element errors
Note: M=『x|x belongs to A』 means that M=A instead of M∈A,
Just as R is a real set,{ x|x∈R} also represents a real set.

Let A, B, C be opposite sides of inner angles A, B, C of △ABC be a, b, c, and a=1, b=2, cosC=1 4, Then sinB =___.

C is the inner angle of the triangle, cosC=1
4,
SinC =
1-(1
4)2=
15
4,
And a=1, b=2,
From cosine theorem c2=a2+b2-2abcos C: c2=1+4-1=4,
Solution: c=2,
Again sinC =
15
4, C=2, b=2,
By sine b
SinB = c
SinC: sinB = bsinC
C=2×
15
4
2=
15
4.
Therefore, the answer is:
15
4

The opposite sides of the inner angles A, B and C of the triangle ABC are a, b and c respectively. Given a=b*cosC+c*sinB1, find B2. If b=2, find the maximum value of the area of the triangle ABC.

As the height of side a,
A=bcosC+ccosB
A=bcosC+csinB
SinB = cosB
B=45°
(2) B2=a2+c2-2accosB
A2+c2-√2ac=4≥2ac-√2ac
Ac≤4/(2-√2)=4+2√2
Ac max.4+2√2
S ABC=1/2 acsinB≤1/2*(4+2√2)2/2=√2+1
Maximum value of triangle ABC area is √2=1