etermine the set of soluti -) z³ = >) 25 = –32i. 2 + 2/3i.

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Q: If n is an odd natural number prove that I =, xsinnx dx = sinx 2.

A: Consider the given: It is given that n is an odd natural number, Take n = 1,Substituting n=1 and…

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A: Here we have been given the measurement of SQ = 22 and S is the centroid.

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A:

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A:

Q: find and classi f1 extrem um points of the func tion flriy)exěsing

A: First we will find all critical points.

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A:

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A:

Q: Exer. 11-16: Express as a trigonometric function of one angle. 11 cos 70° cos 53° + sin 70° sin 53°…

A: Use the trigonometric identity cos(a-b)=cos acos b+sinasinb where a is 70°and b is 53°. cos 70°cos…

Q: Evaluate the 2 intergrals attached as images with the question.

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: IF 2 = +i Sin I) UgE DE MOIVRES THEOREM TO fiND ALL CUBE Roors of 2.

A:

Q: a) Show that: tan z, + tan z, tan(z, + 2) = 1- (tan z) +(tan z)

A: To prove the formula:

Q: How do I get the re the result inside th Lel, tan' (2) = t » tant = 7 Sint it it e Sint = Cit +o)/2…

A: Euler's Identity

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A: Given

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A:

Q: V/ Prove that: (1) tanx= cot

A:

Q: Calculate the area of the circle r = 3 sin θ bounded by the rays θ = π/3 and θ = 2π/3.

A:

Q: Let й -, й- where A and Bare some constants. Given that ü+ 50 = find the value of the product A.B.…

A: A. B=48

Q: Determine the area of the right half of the cardioid formed by r = 7+6 sin 0 14 12 10 8 6 2 -2 -4…

A: Explained below

Q: < sin!!), w5"1)? aiong.seni-circle. 4) Work done by o trom tJ5, 1) to' (-3,-1) t radius 2 · 个。 3+1…

A:

Q: If tan-0 = 1- a Prove that sec® + tam Ocosece = (2- a) 3. %3D %3D

A:

Q: y= COsax tor Osxs T Question,

A: The derivative is calculated using first principle

Q: Evaluate et sin z cos z dr I COS using Simpson rule with h 20

A: Simpson rule  ∫abf(x)dx=h3f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(x4)+⋯+4f(xn-3)+2f(xn-2)+4f(xn-1)+f(xn) Where…

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A: Given; Tan(thetha) = √3.

Q: 2. Prove using the angle sum identity of sine: sin 90° = 1.

A: 2- Given- sin90°=1 To prove- The above expression using sum identity of sin. Identity Used-…

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A: In Euclidean Geometry, the area of a triangle is calculated by multiplying the length of any side…

Q: Find the Valucs of all six trigometfrie Funedion 6) cot x =-, Cos xLO 3, COS

A: cotx=-23, cosx&lt;0 Since both cotx &amp; cosx are negative, therefore x lies in second quadrant.…

Q: 18 sin=+icos- 3.

A: Given complex number is sinπ6 + icosπ618

Q: What is the value of the i in the ex

A:

Q: 2- Prove that: sin(z + w) = sin z cos w + cos z sin w %3D

A: sin(z+w) = sinz cosw + cosz sinw R.H.S  By multiplying 2 from numerator and denominator 1/2 (2sinz…

Q: Solve for x in the figure ALMN is equilateral, and MP bisects ZM. Show all work!

A:

Q: @H-w/ prove that cosiz=coshz

A: We have to prove by using cosiz and coshz formulae.

Q: The center of Dis R. Rare}

A: As the centre of group D4 is {R0,R180}•

Q: 'ove by CO iction that Vɔ 1S tional.

A: Proof by contradiction

Q: Let z=x+iy be a complex number such that coshz#0. Then Im(tanhz) is equal to

A: None of these is correct.

Q: normed spore) is contimous Segpeue HEX. d:x--X(when x is a nome -> i.e

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A: -To show:cos11o+sin11ocos11o-sin11o=tan56oBasic formula needed:-tan(A+B)=tanA+tanB1-tanA.tanB…

Q: secx + 1 51. secx - 1 (cscx + cotx)? %3D 52 56 verify that the equat

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Q: yepriate trigonomic subititution to rewrite the intya) U se in the form E sec'e de

A:

Q: 17) In(v600 cos x +9)= T %3D

A:

Q: Find the concevity. point of infleetion, of fluj n=770 Also explain it jeometrically

A:

Q: Derive the De Moivre's Theorem?

A: The De Moivre’s formula or De Moivre’s Theorem states as: cosx+isinxn=cosnx+isinnxwhere i is the…

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A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find a formula that expresses the fact that P(x, y) is a dis- tance 5 from the origin. Describe the…

A: Given that the p(x,y) is a distance of 5cm from the origin. We need to find the formula to describe…

Q: 9. Use the Residues Theorem to calculate 1+ sin² ª -de. Sketch the contour you used.

A: We have to find integral using Residue Theorem.

Q: Hiw, prove That, The areao f enclosed triangle in figure equa l 121" 2. Hol prove Theet, The area of…

A: Area of right angle triangle is 12·Base·Height . Concept of  Rotation in complex number : If we…

Q: Prove that: tan-¹ z = In( 2 Note: tanz = And sin z = COS Z = ‚i+z. sin z COS Z eiz-e-iz 2i eiz te-iz…

A:

Q: Define Rolle's Theorem. With the help of Mathematica, show the applicability of the theorem en…

A: Rolle's Theorem: Let a &lt; b If f be a continuous function on the closed interval [a, b]  and…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.