cos?x-sin²x cotx-1 e) tanx + tanx f) cos²x+sinxcosx sinxcosx cotx

Q: If ƒ and g are functions then ƒUg is s a function.

A: We need to prove that, if f and g are functions, then f ∪ g is a function.

Q: 3. Given an integer a, then a³ + a² + a is even if and only if a is even. 4. Given an integer a,…

A: As required in the question, detailed proof of 3, 5 and 9 are given as follows :

Q: Use the addition formulas to derive the identities in Exercise

A: Use the addition formulas to derive the identities in Exercise                             cosx+π2=-…

Q: Show that if both f: A ---> B and g: B ----> C are bijective, then g 0 f: A ---> C is bijective.

A:

Q: 1+ sin 0 csc0+1 1-sin 0 csc0–1 II

A: We have to prove the identity.

Q: (3) P(A| B) > 0, i.e., the conditional probability is always non-negative.

A:

Q: d. P = 4x1 – 2x2, Q = 2x1 + 6x2; D is the interior of the ellipse: x1 = 2 cos 0, x2 = sin 0, θε [-π,…

A:

Q: (c) If in (b) |sn < M Vn, then |a1v1 + ... + a„Vn| < Mv1 Vn.

A:

Q: Suppose s and t are distinct natural numbers. Show that lcm(s, t) + lcm(s+1, t+1) > 2st/(sqr(|s −…

A: Given: s and t are distinct natural numbersTo prove: lcm(s, t)+lcm(s+1, t+1)&gt;2sts-t

Q: 8. Complete the following proof. USE HOWEVER MANY LINES THAT YOU WANTO Given: m< 1 = m< 2 m< 4 = m<…

A: It is given ∠1=∠2∠4=∠5 To Prove: PQ parallel RS Proof: ∠2=∠5   (vertically opposite angles)…

Q: W-2. (f g)'(x) = f'(x) · g(x) + g'(x)f(x)

A:

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: Theorem: let S₁, S₂ be the collection of sets D (US) U (US). = US. SES, VS₂

A: Solution: Let S1  and S2  be  the  collection of sets.We  have  to show  that  ∪S∈S1S∪∪ sS∈S2=∪…

Q: 12-4 If M and N are similar matrices (that is, N = some nonsingular matrix P), then oe(N) = oe(M). =…

A:

Q: Evaluate these definite integrals: L, ¢x³ – 3x + 2) dx a. 2e b. S"( cosx – ) dx (Vz – z) dz с.

A:

Q: 8) Suppose A E Mnxn(F) is diagonalizable. Let A1,· , Ak be the (distinct) eigenvalues of A. a) Prove…

A:

Q: Bezout identity of (21,44)

A: SOLUTION -Formula to find Bezout identify:To Find Bézout identity of two numbers, we need to…

Q: x + y)(z + w) = xz + xw + yz + yw A.) Explain in your own words what this problem is asking. B.)…

A:

Q: 29. For any odd integer n, n° n² +3 %3D 4 4

A:

Q: Name the set identity that is used to justify each of the identities given (a) (BNC) UBNC=U (b) AU…

A:

Q: x7= - 3x + 18 JZ - 54 in (3+ 57) + c 3/2 2 dx = %3D 3 + VX 3

A:

Q: The ring Zs[i] has no proper ideals True O False

A:

Q: 9 (b) For cach E70, there exists rational number re(U, E).

A:

Q: Suppose that 0 0. Prove that there is an open set O containing E such that 0m* (0) ≤m* (A) and an…

A: The outer measure m* is a way to assign a non-negative value to any subset of the real numbers that…

Q: Construct a strengthened conditional proof for the following. (M 5 O) > (N ɔ P) Q כ (P כ M) .: Q

A:

Q: 4. Is it more likely that Harper will pick 2 French books or 2 English books? Use the following…

A: 4) Given that there are 2 French books and 3 English books.  Since the number of English books is…

Q: 3. (10 points) a) Use an element proof to prove the following: for all sets A and B, A - (ANB) = A –…

A: The detailed solution is as follows below:

Q: 8. Let V and W be the vector spaces and T : V → W be linear. (a) Prove that T is one-to-one if and…

A: Let V and W be the vector spaces and T:V →W be linear. (a)  Prove that T is one-to-one and if and…

Q: Theorem 5. Abel's Lemma, or Partial Summation Given Sn = a1 + a2 + + an ... (a) a1v1+...+ a„Vn =…

A:

Q: Question Prove that if AUB= A is true, then ANB = B is also true, AND CONVERSELY. %3D

A:

Q: State and Prove Pick’s Theorem.

A: Let P⊂ℝ2 be a polygon with all vertices on lattice points on the grid Z2. Let  I be the number of…

Q: 2. Use the principle of mathematical induction to prove that (2n)! n! n II (4k-2) = k=1 for all n E…

A:

Q: rove the identities for 7and 8

A: we have to prove the identity ,  a) sin3π2+x-sin3π2-x=0b) sin(A+B)+sin(A-B)=2sinAcosB

Q: There exists two odd integers whose average is odd. 1 1 1 There exists distinct positive integers a,…

A: (a) Consider two odd integers 2m+1, 2n+1 such that m+n is even. Now, Consider the average of the…

Q: Every cyclic group is necessarily abelian but the converse is not necessarily true

A: .