For Exercises 59–60, use the sum-to-product formulas to verify the identity. 59. сos + t - cos 4 -V2sint 4 60. sin e + sin e + 4 VZsin e 4

Q: 37. ; with r = 1 andh = ;: 0, p2 sin¬! V1-h² /r²-h/r2-n? (0,, 33 47-3/3 (0, 0.71)

A: Let's simplify in steps Let's take the numerator first:

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Q: (iii) 1 dø -sin²Ø Hint: may start with de (T(1/4)} /2 Vcose to obtain the result

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Q: Suppose z and y are funetions of time and satisfy the formula e sin y = In y + tan dy Write a…

A: Solution:- differentiate with respect to t.

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Q: "ind no E N such that for all n > no sin(n + n² cos(n²)) n3 – 5n4 – 20 -

A: Find n0

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Q: Hence, using chain rules find y' i. y = sin(2x² + tan(6x² – x)),hint: u = 2x² + tan(6x² – x) ii.y =…

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Q: Answer: The approximate value of sin 29° is O sin 29° s 1( 29x 2 180 6)+ O sin 29° V3 ( 29x O sin…

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Q: b) Is S cos4xv2 – sin4x dx = V(2 – sin4x)³ + C true or false? show me %3D

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Q: By the samc way, prove that g 7 sinw.k MUIS Z N-27 cesW. +1

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A: Given,y(x) = C1 sin2x + C2 cos2x + 1 — (1)Here we find the value of C1 and C2 such that the equation…

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A: We can prove given result by mathematical induction: Define a statement p(n).  Show that p(n) is…

Q: 18.) Suppose x = R cos(0) sin($), y = R sin(0) sin($) and z = x² + y? + z? = R²Y R cos(). Verify the…

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Q: (c) Integrate sin"uelog (cosu) . Where n is 482

A: Integrate the sinnuelog(cosu). Where n=482

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Q: (1 + cos 9t) 2 sin 9t dt

A: ∫0π1+cos9t2 sin9t dt Consider, ∫1+cos9t2 sin9t dt Put, 1+cos9t=u⇒0-9sin9t=dudt⇒-9sin9t dt=du⇒sin9t…

Q: The integral S (A S- (в x dx x² + √√√x²-1- sino do 1 + cos sec²0 do 1+tano " cose de 1-sino sece…

A: Use trigonometric substitution

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Q: ,In sec2(sin2y)dy can be evaluated by writing it as sec2y (A @ In sec2( sin2y) · cos2ydy ®/…

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Q: The suitable substitution to evaluate the integral cos°(2x) dx is 5(2x) 3 csc°(2x) u = sin(2x) u =…

A: First, simplify the integrand and use the substitution method

Q: 0. If 180° < 0 < 270° and cos e = -, find sin 20. %3D 13 O- 16V105 169 O 16/105 169 O sV105 169 O -…

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Q: The suitable substitution to evaluate the integral tan (2x) dx is cos“(2x) none O u= csc(2x) O u=…

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A: Complex integration of the function

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A: Given y=(cos(x))^(cosx) Now differentiate y with respect to x

Q: In Exercises 47-52, use Eq. (12) to find N at the point indicatee 47. (12,1), 1 = 1 %3D 48. (t- sin…

A: The solution are next step

Q: In Exercises 17–20, find dr/d0. 17. r = 4 – 0² sin 0 18. r = 0 sin 0 + cos 0 - 19. r = sec 0 csc 0…

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Q: In order to evaluate Vx2 - 6x + 45 d, the correct substitution is Ox = 6 – 3 tan(t) O x = 6 + 3…

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Q: Solve the eaation on the interval. 2sin Đ =3(cos o t D

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Q: 0, o° s 0 < 360°, given the follo Cos e = and 0 in QIII 2.

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Q: If f(x,y,z)=In(x²y+sin?(x+y))+111x112y2z113, then at (1,1,1) is equal to əx²əyəz

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Q: Find a closet rank-1 approximation in the (2 cos 0 - sin norm to A = sin 0 cos e

A: Consider the provided question, The l2 norm or Forbenius norm(FN) is the square root of the sum of…

Q: Express Q(x) = cos4 (x )+ 12 as the composition of three func-tions; that is, identify f, g, and h…

A: Q(x) = cos4 (x )+ 12 We need to express the given function as a composition of three functions  that…

Q: ,In sec²(sin2y)dy can be evaluated by writing it as sec2y ! / sec²( sin2y) - 2 cos2ydy S. | sec2(…

A: To simplify the given integral.

Q: Differentiate implicitly to find 04 0-3 O 3 3 cos(y+z) 4 cos(y+z) Əz Əy 2 given 4x + sin(3y+z).

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