If xr = cos(л/2") + i sin (л/2"), Show that X1X2X3X4.....Xn = COS lim x1x2x3x4......xn= s [π (1 − 1)] + i sin [π (1 − 1)]. Hence show that

Q: 1. Find the derivative 4 ln 2) ³ 3x³ sin(2x) 5x2+3

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Q: cos(: sin@)]=[- sin(esin@)]. * (b) (i) Show that - cose dt

A: We will use product rule of differentiation here

Q: e (a) S sin* x dx

A: Apply reduction formula:∫sinnx dx = n-1n∫sinn-2(x)dx - cosx. sinn-1(x)nwith n=4∫sin4x dx =…

Q: Let Express the value of in terms of I. pn/12 0 tan ¹2 (2x) sec (2x) dx I = p/12 10 S tan ¹0 (2x)…

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Q: Differentiate the following function COS T 1 (a) sec(x) tan(x) (b) (c) sin (4x° + cos(x))

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Q: Use  DeMoivre’s theorem  ( Cos(x) + jSin(x))n = Cos(nx) + jSin(nx) to show that Sin3θ=3sinθ- 4…

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Q: Q1) Show that: (b) (cosx) = -sinx =1+* (a) (1+x) =1+6x %3! (e) (VF) = (d) v1+ tan x

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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Q: cos( 2 sin1 (X/17)) = Select one: O 2x ( 289 - x )o./ 289 O ( 2x - 289 )/289 None O 34 x/( 289 + x)…

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Q: sin x+3 cosr dx. Determine the following rational function 1+cosx

A: We have to first do partial fraction of the given expression.

Q: sin x cos" п — 1 n 2 2, | co cos"-2 x d.x Show that for cos" x dx Use this to find cos4. x dx.

A: Given, ∫cos4xdx

Q: Find the first derivative of y = Arc tan √x² −1+ Arc csc x 2 O 2 O 0 2 Ox√²+1

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use  DeMoivre’s theorem  ( Cos(x) + jSin(x))n = Cos(nx) + jSin(nx) to show that Sin3θ=3sinθ- 4…

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Q: 7) {(1- sin° 31)- cos3t dt 8) | t in’ (5x)· sec´ (5x) dx

A: 7) I=∫1-sin2 3t·cos 3t dt  ……1

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: 3.(1) Show that (x) - J{«) )x cos 2.x

A: Consider the Bessel function, Jnx=xn2n Γn+11-x222n+2+x42·42n+22n+4-…             ...1 Substitute…

Q: b) Differentiate the function below with respect to x. f(x) = (2+3x) sin (8 + 2x) Note: In Text mode…

A: The given function is f(x)=-2+3xsin8+2x. To Find: Derivative of above function.

Q: cos(2x)–1 lim x'+ 5x ? 3

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Q: w= Cos (x+y) + Sin (X-4) Show that dy?

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Q: Prove that for all positive integers k < n, the equality n n n =2n-k k k i=k holds.

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Q: 0 a "/2 ((+ cos@)-1)sin@d0 + a |((1+ cose) - 1)sinede 3 3 a ("/2 (1+3cos@+3cos 0+ cos 0-1)sin@de a3…

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Q: Compute | a° sin(æ" + 2) dæ.

A: Given : ∫x6sinx7+2dx

Q: Evaluate sin[arccos(−1) + arctan(−1)].       Your result should be in exact values (do NOT use your…

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Q: 4) Verify. cos²(x)[1 C. – tan²(x)] = cos(2x)

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Q: What is the VaR Controversy?

A: VaR controversy in football keep proving that technology may not be the saviour. VaR offside…

Q: Choose the correct answer If f(x)=ln⁡(cos⁡(3x)) , then f"(x) =…  -9 sec2 (3x)  9 cos2 (3x)  9 tan2…

A: Derivative problem....

Q: sin5x(1-2t)dt (6) lim

A: limx→0∫xsin5x1-2tdtx Let  I=∫xsin5x1-2tdt=t-t2xsin5x=sin5x-sin25x-x+x2

Q: Find sin(x/2) =  cos(x/2) =  tan(x/2) =  Given tan(x) = 2sqrt2    0 degrees < x< 90 degrees

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Q: If f(x) = sinx + cosx sinx - cosx 2 show that f'(x) = sin 2x – 1

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