1. Suppose coS(a – B) and cos B 5 25 If P (a – B) is in QIV and P (B) is in QIII, find the values of the following: (a) sin(a – B) (b) sin B (c) sin a (d) tan (α-2β)

Q: 1 + sin 4x cos 4x + C 8. 13.

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Q: 24 cos 4x – 32 sin 4x а. (с, + 4x) сos 4x + (c, + 3х) sin 4x b. c,e2x + C2e 3x + 3 sin x C. none of…

A: follow the next step

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A: Given that we have to prove where

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Q: 1. Eliminate the arbitrary constants of the given equation y = C₁ cos 3x + C₂ sin 3x + C, sin x + C,…

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Q: (a) If = cos (2x), then y= xp (A)cos (2x)+C cos* (2x)+C (C) sin(2x)+C 2. 2. 2. (D) sin (2x)+C (E)…

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Q: sinx S- cos?x+ 6cosx+13 O In cosx+3-Vcos²x+6cosx+13|+C O In cosx+3+/cos²x+6cosx+ 13 O…

A: To find:

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Q: If e /2i -sin2 then z = - 2 In(sin2) + 4KTO - 2i In(sin2) – 4kT 2i In(sin2) + 4k TO - 2i In(sin2) +…

A: Given e(-z/2i) = sin2 We need to find z. The solution is given below.

Q: 36. (a) Prove the reduction formula 1 cos"-'x sin x + п S cos"x dx = | cos"-2x dx n n (b) Use part…

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A: We have the relation,                cos2x+sin2x=1   If sina=48= 12                 cosa=1-sin2a…

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Q: 3. Find g'(x) if g(x) = sin³(4x) %3D A. cos (4x) B. 3 sin?(4x) cos(4x) c. 12 sin (4x) cos(4x) D. 4…

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A: Given query is to find the integral after substitution.

Q: if x <1 x – 1 | f(æ) = T In x -) if1<x < 4 4 In 2 %3D a cos 27rx + b sin( 2" if 4 < x | where a and…

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Q: 4. (a) Express 3cos x-4 sin x in the form R cos(x+ a) where R>0 and 0 <a < (b) Hence find the…

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Q: If L{cos(ax)} then find L{x³ cos(ax)}. %3D p2+a²

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Q: 32. If 2 sin 0 cos 0 cos 0 =0, where 0 <0 < 2n, then the exact values of 0 are 57 0, 3 O0, 5. 7, ,…

A: Given : 2sinθcosθ - cosθ = 0 Where, 0 ≤ θ ≤ 2π To find : Exact value of θ?

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Q: 1.14 To determine L sinh(3t)cos (t) , f(t) = sinh(3t)cos? (t) must be rewritten as %3D - e sinh( 3t)…

A: Laplace Transform Definition: Given a function ft defined for all real t≥0, the Laplace transform of…

Q: 9 Find 0 if 0<0 < 2n and: d sin 0 = 1 h cos? 0 = i tan 0: i tan? 0 = 3

A: To find θ if 0 ≤ θ ≤ 2π  sin θ = 1cos2 θ = 12tan θ = -13tan2 θ = 3

Q: (1) Evaluate the following functions 1. In(3-i6) 3. cos (1+i3) , 2. e(0 52) , 4. tanh (2-i5)

A: As per guidelines, we solve only first question. 1. Given      ln3-i6

Q: 1.4 The integral 2 sin (15ax) sin (10a.x) dx equals: (a) (cos (5ax) – cos (25ax)) da (b) (sin (5ax)…

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Q: 3 6. Show that [[[ y sinzdxdydz = (1– cos1). 2 COS %3D 00

A: We have to prove given integral

Q: 1 with in Ql , find sin B = B If cos B B Cos 3- 2/2 6 3- 2/2 Cos B COS 22 3 B cos 3 + V3 3 + 3 Cos 6…

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Q: 2 (t) ST ST Problem 8.1 It is known that n(t) - a + bi sin wt + az cos 2ut + as cos dut + ...

A: Consider the given equation:…

Q: 9/8 2* CoSメーenp and X=/t+] its dus

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: 5. Find the exact solution to 3 cos-1 x – n = 0.

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Q: S cos(3z)sin1º(3z) dz A 1 (sin(3z))10 + C 3 C 1 (cos (3z))10 + C 3 -- 1 D 1 (cos (3z))'1 + C 33…

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Q: Find the general solution for cos^2 (x) = 0

A: Cos2x=0Cos x=0x=π2,3π2,5π2--

Q: 2л 4) Find | cos 0 d0 using Beta function.

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Q: Зл ,2n) then tg 2 1 If α te( V1- cos“(a – n) + a)+ = 0. 3n – 2a sin(5n + a) 1- sin 2

A: We have to prove the trigonometric equation.

Q: Suppose that sin(a) = 4/5 and cos(b) =4/7 define in the first quadrant, determine tan(a+b). (round…

A: Given, sin(a) = 4/5 ------equation 1 cos(b) =4/7 ------equation 2

Q: 12. If f(x)=sin(2x+1), then f'(x) is equal to A -2 cos (2x+1). 2 cos(2.x+1). 4 cos(2x+1). C D -4 cos…

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Q: For cos2(xy) = - evalu COS 4

A: Given

Q: 7.32. Prove that for 05sr, -( . ) cos 2 cos (a) a(e -a) = sin 3r sin ba (6) (r-) - 7.33. Use Problem…

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Q: (1/2 3. x coS TX d Jo

A: Consider the given integral, ∫012xcosπxdx To solve the integral, apply the By-part rule of…

Q: Find cos (0 + p) given that cos 0 = 2 and cos p = 2 and that 0 and p are between 0 and t/2.

A: For the given values of  Cos(θ)=1213 Cos (ϕ) = 35 Cos(θ+ϕ ) is evaluated as shown below

Q: 10. If y = sin 2x + cos 2x, then (yn)o is equal to nn a) (-1)"2" b) 2" c) sin+ cos d) None of these

A: The solution is given as

Q: 1 In 3n 1 sin (3x) [cos"-1 (3r) sin (3r) + 3(n – 1)In-2] %3D I1 = %3D - 3 What is I, ?

A: Given : In = (1/3n)  [cosn-1 (3x) sin (3x) + 3(n − 1)In-2 ]  I₁ =  (1/3n)sin (3x)

Q: 2. Find the exact value of cos 30°. Enter your next step here () d号

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Q: 4) Find when y2 – x² + cos(x + y) = 0

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Q: 3 Find all solutions of cos 2x for x if 0 < x < 2n. 2

A: The solution is :

Q: b. cos(3n) + 2 sin(3n)

A: Solution :-

Q: 2 35 sint x cos³x «

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Q: -1 Find y' where y = 22 sin-(cos (9 æ)) – tan (6 æ) Answer: -198 sin(9 x) 1 || V1-cos2 (9 æ) 1+36 x2…

A: To find y'

Q: -1 (x³+y³ ,3. then xdw dw +y dy If w = tan x-y sin(w) sin(2w) cos(2w) None of these

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Q: 16. Evaluate S x² cos(x³) dx a.) -sin(x³) + C b.) sin(x') + C c.) - sin(x³) + C d.) sin(x') + C

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