Which of the following identities is not valid? O None of the choices À ·B = B · Ã ад ав — сos @AB č · (Ả x B) = -B · (Ã xc) -B • (Ã × Ĉ)

Q: Which of the followings are false? I. General term of (2,3,2,3,..} is a, =+ (-)". L General term of…

A:

Q: Which of the following is equivalent to expression cosh?u- sinh²u? (A) 2e-u (B) cosh2u 2e" D none of…

A: Using the formulas of coshx and sinhx

Q: Determine if the statement is possible for some real number z.     sin z = 1.2

A: Given: sinz=1.2

Q: Which of the followings are true? 1. General term of {(2,3,2,3,.) is an =+(G)". II. General term of…

A:

Q: D F L K Name the congruence theorem Your answer: O AAS O ASA O SAS

A: Given data: ∠D=∠J∠E=∠KDE=JK Therefore, ∆DEF≅∆LJK by angle side angle.

Q: 30) for nz I derive each of the identities belaws %3D

A: Given : n0+2n1+22n2+⋯2nnn=3n

Q: Which of the following identities are correct? Choose all that are correct. O et+y = e¤ + eY O e+Y =…

A: We know that; The exponent rule: 1). axy=ax·y 2). abx=axbx 3). ax·ay=ax+y 4). ax÷ay=ax-y 5). a-x=1ax…

Q: Using the definitions: sin(z) = (e^iz - e^-iz)/ zi  and cos(z) = (e^iz + e^-iz)/z Prove that  sin…

A: Using the definitions: sin(z) = (eiz - e-iz)/ 2i  and cos(z) = (eiz + e-iz )/2 We need to prove that…

Q: Which of the following identities hold? Select all that apply. Your answer: 8 13 + 3993 2 T In 1+ 11…

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Q: 1 If x= tand , then dr coso do . (1+x²) ½° A True B False

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Q: #1. Evaluate (4cis #2. Given Z1 = 5 (cos 15° + i sin 15°) and Z2 4 (cos 120° + i sin 120°) Z1 a.…

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Q: Which of the following function is not harm Select one: COS z CO Re(- Cos z o Im () Re (2) sinz o Im…

A: Note that if f(z) is an analytic function then real and imaginary part of f(z) are harmonic. Note…

Q: Fiven: LM NO; ZLMO = ZNOM Prove: LO = NM Reasons

A: Given that: LM=NO, ∠LMO=∠NOM

Q: Which of the following four statements establishes the identity? O A. 1 1 cos X 2 Csc x sec x= cos x…

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Q: Evaluate: o So" cos)dzdzdy COS O 4 (T- 2) (T – 2) O 47

A: Topic : Definite Integration  Correct answer:-  option 3

Q: 3. Prove or disprove: (a) a bc = a | b (b) a | bc and gcd(a, c) = 1 =→ a |b (Hint: recall Bezout's…

A: We have to check whether given statements prove or disprove.

Q: Prove that the following statements are i0 (sin 0+ cos 0)' =1+2sin 0.cos 0 cos e (a) 1 (b) tan 0 sin…

A:

Q: Which of the following is NOT a sum or difference identity? sin(A+ B) = sinA cos B + cos A sin B B…

A: Trigonometric identity: The standard sine sum identity is:sin(A+B)=sin(A)cos(B)+cos(A)sin(B)

Q: the followking identity. us-1/1+_A Prove

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Q: 14) Prove that the following is an identity: (x +y)³ = x³ + 3x²y+ 3xy² + y³

A:

Q: Prove or disprove the following identity: det (cA) = c" det A %3D

A:

Q: csc2 3. cscr ² z + cot² r 1 - cot r Cse

A: As we know                      Cosec2(x) = Cot2(x) + 1

Q: Which of the following situations is very much useful in proving identities

A: To answer the given question about identity.

Q: Prove the following identity: (x + y)2- (x-y)? = 4xy %3D

A:

Q: Which of the following is equivalent to 24 f /4- da O none of these • 12 f(1 -cos 0) dº O 24 f (1 -…

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Q: 1) Prove the following identity: (x + y)² – (x – y)² = 4xy

A: Consider the given identity. x+y2-x-y2=4xy   The square of two numbers difference and addition is…

Q: 2) Prove the following identities: (a) A\B = A\(A O B); (b) A o (B\C) = (A O B)\CA Q C) = (A O B)\C.

A:

Q: • Prove or disprove the following identity: [cos me -sin me] sin me cos m0

A: Given that , Tm=cos mθ-sin mθsin mθcos mθ  We prove this theorem by mathematical induction method,…

Q: Verify the following identity. sin 0 Cos Which of the following four statements establishes the…

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Q: Which of the following can you not use to prove A CAT S A DOG? 1. CA DO II. ZC ZD III. ZA E ZOo IV.…

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Q: Which of the following identities is/are not valid? Ĉ. C (ẢxB) = −B (Ảx©) aAaB = COS AB more than…

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Q: Let m be a real number. Then 2(sin (mx) + cas¯ (mx)) = mn 2(sin (mx) + cos (mx)) = n -1 %3! The…

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Q: Give an example of two denes not equal X subsets of (R,T) and (z,7or ). ( Explain your answer ). cof…

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Q: Evaluate: o So² i p³ sin o cos pdpdøde . 827 16 817 16 817 18 817 13

A:

Q: 1. Show that 0* = 0, I* = I. %3D

A: Matrix

Q: Determine if the statement is possible for some real number z. sin t = z possible O not possible

A: We have to find out z

Q: 1. Evaluate each of the following using appropriate identities : (a) (a? + b2)2 (b) (xy + 2z) (c)…

A: The following identity will be used for the given questions x+a2=x2+2ax+a2 x-a2=x2-2ax+a2…

Q: Prove the following identities as shown.

A: Given: verify the identity sinucosecu+cosusecu=1 we know that  cosecx=1sinx…

Q: (a) Evaluate 1 2-i) and Σ > sin nT i=-4 n=1

A: a) Given : ∑i=-41 i2-i We get  ∑i=-41 i2-i=-42--4+-32--3+-22--2+-12--1+02-0+12-1∑i=-41…

Q: If Cov(x,y) = 0, then X and Y are uncorrelated Select one: O True False

A: If two variables are independent then their covariance is zero and we, say that they are…

Q: 5). Determine whether the following ODE is exact, if it is exact, solve it 1 - + cos 3r fip dr 2y 4r…

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Q: 3 Show that sin 0: 8. 1 cos (20) + %3D cos (40). 8 Which of the following four statements…

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Q: Prove the identity below. sec? r + csc² r = (sec² x)(csc² x)

A: We have to prove the identity sec2x+csc2x=sec2xcsc2x.

Q: Int) If A = then det( A) = Is Choose A-= and det( A-1) =

A: The matrix is A=16-71

Q: Verify the following identity. +e = sin 0 2 cos Which of the following four statements establishes…

A: Given identity as cos3π2+θ=sin θ Use the formula as cos A+B=cos A cos B-sin A sin B

Q: For each of the following identities, write down the exact mathematical statement and prove it (we…

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Q: Differentiate which of the equations are identities, if they have one solution, or no solution. Show…

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Q: Prove that the following identity is true. 1. 2 csc? x 1+ cos X 1- cos x X

A: I have given an answer in step 2.

Q: Verify the identity. cot 2 cot x+ csc 2 x= 1+2 cot? x Which of the following four statements…

A:

Q: Verify the following identity. cos = sin 0 Which of the following four statements establishes the…

A: To verify the formula  Cos (π/2 - θ) = sin θ

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.