7. We recall that in lectures we used the notation (PQR) to mean the area of triangle PQR. With this in mind, consider a triangle ABC. Let D be the midpoint of BC and let E be an arbitrary point inside the triangle ABD.

Q: Prove that AAB = (AU B) - (An B),

A:

Q: 1. Explain why Corollary 1 of Theorem 9-7 is true. That is, explain why L1 = L2.

A: Given that ∠1=∠2 is true statementsHint: Major arc; Minor arcand…

Q: Prove. Z40 (Rez) ² +Z1 ? 0

A:

Q: Prove that (x - i) = > xi i=1

A: We will prove the following result.

Q: 1+ sin 0 csc0+1 1-sin 0 csc0–1 II

A: We have to prove the identity.

Q: Construct a proof that ZEIF = ZGIH. н

A:

Q: What does the Theorem of Pappus say?

A:

Q: show that (to) arg = = argz

A: We have to show that  arg z¯ = -arg z.        ...A     Let us first see what is z¯, z¯ is conjugate…

Q: Show that im n /-

A: Limit of the sequence

Q: 2. Show that cÃ=cA.

A:

Q: Suppose B = (9, 2) and AB = (11, 4). Then A = %3D

A:

Q: Show that if a > b, and a, b i= 0, then b- 1 > a - 1, provided that a and b have the same…

A:

Q: prove that div A マ - Kr

A:

Q: How many counterexamples are needed to prove that a statement is false?

A: Suppose P(x) be the statement.

Q: 1)r =4rsin e

A:

Q: dz

A: Wallis FromulaFor  positive integer n∫0π2sinn x dx=∫0π2cosn x dx       If n is even   1.3.5. ...…

Q: Show that (AB)¹ = BTA¹ if A = 2 0 2 0 and B = -1 1 15) -3 1 -1 -1 2 2). a

A:

Q: Let A = {5, 10, 15, 20, 25) and B = {3, 6, 9, 12) (a) Find A - B (b) Find B A (c) Based on your…

A: we know that A-B=A\B=all those element of A which are not in B.Simialrly, B-A=B\A=all those element…

Q: Prove that if r>3 and y > 4, then ry > 11.

A:

Q: Evaluate iy ( + + " ). Nin t

A:

Q: verify that (AB)T = BTAT

A: Given matrices: Now,

Q: Find b if a = 9

A: Given that OA=2 , AB=3 and OC=a=9 b=? Let ∠DOC=θ

Q: If xly, then show that ||x+ y|| = ||x- y|!.

A:

Q: What is Rolles Theorem and how do you find "c"?

A: What is Rolle’s Theorem and how do you find c

Q: State and prove Littlewood's Third Principle

A: Littlewood's Third Principle, or the law of iterated logarithm, can be understood intuitively as…