a=D cos-(p+r)+ a ? an(r-p)cos(r-p), which of the following would be equivalent to 14 14 9. 3 3 (A) cos psinr (B) -cos psinr (C) cos r sin p (D) cos psinr (E) cosrsin p 35 10 35 7 10

Q: -p² sin(w) cos?(w) – p cos² (») -p2 sin(4).

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Q: 4 cos (m) – 4 cos (m) +1 sin (m) 2 dm

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Q: A4 to Select the TWO expressions that must be equivalent to cos A. tan 90 B. sin z sin y

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Q: V3 If sin (A+B)=1 and cos(A-B)=,0B then find A and B

A: *Given   sin(A+B) = 1    and    cos(A-B) = √3/2  Condition   0<A+B≤90°  and  A>B

Q: d²y If x=5+ cos20 and y=3- sin20, what is ? dx² A csc ³20 (в B - cot20 Ⓒ-csc ³20 D cot20

A: Given: x=5+cos2θ and y=3-sin2θ Now, dxdθ=d5+cos2θdθ=-2sin2θ and    dydθ=d3-sin2θdθ=-2cos2θ Now…

Q: Which of the following formulas are NOT correct? Choose two(2) answer sinA sinB =-1/2…

A: We can write the correct option as below

Q: Q4/ Find the value of the following: cos (tan-1 1) 1) sin (sin-) 2) 3) tan - (cos n) 4) cos(sin)

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Q: What must be the value of A so that cos(r + y)- cos(r-y) = A sin a sin y? %3D O 2 no correct answer…

A: In trigonometry, cos(x+y)=cos x·cos y-sin x·siny and cos(x-y)=cos x·cos y+sin x·siny

Q: 10 -dx may be written as Aln|secB"+ tanB"| + c where A, B, and C are constants not equal to zero.…

A: The given integral,         ∫10xcos 10xdx

Q: V5 3 If cos(a)= and sin(B) = 풍 <a<nand 2 * <B <27, compute the exact value of the following: with 5…

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Q: 10* -dx may be written as Aln secB*+ tanB*|+ C, where A, B, and C are constants not equal to zero.…

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Q: What must be the value of A so that sin(x +y) – sin(x-y) = A cos e sin y? O -2 O 2 O no correct…

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Q: If sin x = A + B cos 2x + C cos 4x, then A = 2 B " с =

A: Since you have posted multiple questions we will answer first problem for you for remaining please…

Q: 10* -dx may be written as Aln secB*+ tanB* +C, where A, B, and C are constants not equal to zero.…

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Q: Using an appropriate substitution, ſ sinº(x)cos³(x)dx is equal to: 10 coslx cos°x sin°x sinx + C 9.…

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Q: V3 For number 4-5: Given sin a = and cos ß = -;, a is in the second quadrant and ß is in the third…

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Q: 10 dx may be written as Aln secB*+ tanB*+ C. where A, B, and C are constants not equal to zero.…

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Q: f(x) = cos(2x), then f'''(pi/4)

A: Given function is fx=cos2x.

Q: Find cos(s - t) given that cos s = -5/13 , with s in quadrant II, and sin t =15/17 , with t in…

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Q: 3 with t < a < - 5 Зл and Find the cos(a + b) given that sin a = 7 with 0 < b < 11 cos b %3D 2

A: We get cos a=1-sin2 a=1--352=1-925=1625=±45 As a lies n third quadrant, we get cos a=-45.

Q: 37 where < < B <2r, find cos (a + B) 2 a<n and cos B = - where Given tan a =

A: We have cosα+β=cos α cos β - sin α sin β tan α=-43⇒cot α=-34⇒cosec  α=1+cot 2α=1+916=2516=±54sin…

Q: n(x-) = A cos x, then the number A is equal to . А. л B." С.О D. -1

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Q: 9. Decide whether or not the following equations are true or false: e° = cos" r + sin² r = cosh? r –…

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Q: 3n determine the exact value of 2 3 2, where <xsn, and cot y = where 7< ys. 5 3. If cos x 2 12 cos…

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Q: 8x O B. [5 sin 5x + 8 cos 5x] + C 89

A: The given integral is, '

Q: (a) sin(e/2) (b) cos(e/2) (c) tan(8/2)

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Q: If x= cos t and y = cos 21, then (sin t 0) is (A) 4 cos t 4y (C) (E) -4 cot t (B) 4. (D) -4 Select…

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Q: QProve that: (Cos 38 Cos3e -3 Cos e Sin e)

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Q: If cos 0 = -- and T < 0 < 3, what is the value of cos () ? 3 V14 V 14

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Q: (i) Express -5 sih 0 + 12 cos 0 in the form R cos(0 + a), where R>0 and 0<a < n. Give the value of a…

A: Okay I am solving first question as you mentioned.

Q: What must be the value of A so that cos(x +y) + cos(x y) = A cos x cos y? %3D О0 1/2 О -1/2 no…

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Q: (a) cos t (d) sec t (c) cot t cos B 1- sin B (c) sin B-1 (b) tan t (e) csc t 9. Which answer is…

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Q: 2. Which equatien will sllewes to sahve fer x? a sin 40= b sin 40 C. Cos 40 d. cos 40 e t 40= L t 40

A: :

Q: Using an appropriate substitution, S sin2°(x)cos³(x)dx is equal to: cosx cos°x cos13x cos1x + C 11 -…

A: Take substitution of Sinx=t.

Q: The f sec$30 sin 30 d0 is {A} sec*30 + C 12 {C}-cos*30 + C {D}cos 30 + C 12 {B} sec 30 + C 18 18

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Q: 2/5 If cos a = and sin a < 0, find the exact value of cos (a +) Show the formulas you are using.

A: The trigonometric function value is given by cosα = 255 and sinα&lt;0 To evaluate : The value of…

Q: 24 where 25 3T < B < 2n , find If sin(a) = where 0 < a < 13 and cos(B) = 2 (b) cos(a – B) ( 1) tan…

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Q: 20 where 29 7E where 0 < a< 17 and cos(B) 37C < B < 2n, find the exact values of the following. 2 If…

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Q: What is the value of x? √2 cosx-1=0 2sin3x+1=0

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Q: If P = A sin 0 + B cos 0 and Q = A cos 0- B sin 0, find the value of A2 + B² in terms of P and Q. А.…

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Q: V3 If sin (A+B)=1 and cos(A-B)=,0B then find A and B

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Q: Find cos(A - B). cos A = V10 and sin B = ,where 0° <A<90° and 270° <B< 360°. 10 O V10-3 30 20 O…

A: Given query is to find cos (A-B).

Q: 20. If cos 0 = 0.2, then cos(8 + T) = 7 %3D A. 0.2 B. -0.8 C. 0.8 D. -0.2

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Q: The

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Q: b) Explain how you would find sin" x cos" x dx if i) m is odd and positive, n is odd and positive,…

A: Solutions

Q: 2. A c² B c(cos 20 + i sin 20) C Cos 20 – i sin 20 D c(cos0 – isin 0) ? (cos0 -+ i sin 0) B D CO

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Q: 2. If sin a =,0<a< 3. 2V5 ,where <B < 2n 3 . cos ß = Determine the value of a. sin(a + B)%3D b.…

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Q: Suppose that (ax + b) cos x dx = -4. What is the value a? cos x a) a = -2 b) a = 4 c) a = 2 d) a =…

A: We can find the value of a as below

Q: 5.) Select which ratios are equal to cos(x). A XO to C a. sin(y) b. sin(90-x) c. cos(90-x) d.…

A: We need to find which ratio is equal to cos(x)

Q: 3. Determine the corresponding reciprocal ratio that corresponds to cos e= 0.8. а. sec e= с. sec e=…

A: 3) Given: cosθ=0.8 To find: The corresponding reciprocal ratio that corresponds to cosθ=0.8.

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.