Express the following in the form r(cos 0 + i sin 0), - < 0 ≤ π: (1 - i)(√3+ i) (1 + i)(√3-i)

Q: Q1\ Answer only two of the following questions: A\ Evaluate f sinx esecx cos²x dx. [15] [8 4 3 1 B\…

A: We have to solve the given problems.

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Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

Q: 12 A A10. If B then the values of A& B =. %3D (x-2) (x+4) x-2x+4 A 2, – 2 b) -2, – 2 c) 2, 2 d) -2,…

A: Since you have posted multiple questions we will solve the first question for you. If you want any…

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Q: a) Use the definition of the hyperbolic functions to prove that 2cosh?(x)–1=cosh(2x). 1%3D

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Q: Exercise 3 The function f (x) = cos(2x) – x has: a) At least one root between 0 and b) A unique root…

A: given function is                                              f(x)=cos(2x)-x we have to find roots…

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A: To find the value of given integral.

Q: Show that sin 3x and cos 3x are orthogonal on [−π, π].

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Q: Ql:- Calculate the expression sec3.42x-5 +In4 cos30)2-4x 2 where x = 2, y = 5.…

A: Topic-Function

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Q: (10,00 Puanlar) Let f(x) = sin 2x. Then find f (999) (x). a) 2099 cos 2x b) – 2099 sin 2x - c) –…

A: Given: f(x) = sin(2x) To find: f999(x)

Q: [1] S(4x³ + x)V4x² + 1dx > [2] S(2x7/2 – vx)* d. [3] S V1+ 2sin3xcos3xdx

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Q: Compute 2 sin x dx -2 4 1 -1 2] O O O

A: Answer is- Option 3 is correct Explanation is given below...

Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

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Q: The principal part for a) 5 b) 2 for xo of f(x) = 2 + 5+ sinx with respect to ↓

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Q: x is in the interval [0, 2t) * sin2x - cos2x = 0 COS

A: Given: sin2x-cos2x=0; x∈[0,2π) We know that cos2A-sin2A=cos2A…