3π b) sin 20 + cosθ = 0,0€ [0, ). 2

Q: 7. Prove: sin(t) dt sin(1) + cos(1) 4

A:

Q: Do the functions y, = cos4t and y, = sin4t constitute a fundamer %3D The functions constitute a…

A: The given differential equation is y''+4y=0 the auxiliary equation is D2+4=0 D2=-4D=±2i therefore…

Q: - 1, z = cos-

A:

Q: Find all values of x in the interval [0, 2?] that satisfy the equation. 6 cos(x) + 3 sin(2x) = 0

A:

Q: Show that 2 sin 0 + sin 20 sin 0 1- cos 20 1 cos e Prove that (G) 1 T 1 tan-1 + sin V5 3. where…

A:

Q: 3. у %3D In(5 — е**) 4. x = et (cos 2t + 2 sin 2t)

A: Now the first given function is ln5-e4x The second given function is x=etcos2t+2sin2t To find the…

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

A:

Q: 5. Find all solutions to 1+ sin sin 3x = cos cos (0.25x) such that xE[0,r]

A: The best way to do this is to use some numerical method to solve this. It is not feasible…

Q: Prove that: 2n 1 cos=0 + i sin 0) + 10 2cosne - %3D eino

A: If  is an exponential form of a complex number where x and y are real numbers then its polar form…

Q: 3. Prove that the identity is true. sin*t- cost = tan²t-1 cos't

A:

Q: b) sin 3x 3 sin x – 4sin3 x [Hint: sin 3x sin(2x + x)] Prove

A:

Q: 3. Show that the equation 1 + cos(x) – 2sin(=) = 0 has a solution in the interval [0, 7 /2].

A:

Q: Find , where : = sin (x²) cos (y) COS 6.x sin (a) cos (y) 2.x sin (a) O2.x cos (2) 2r sin (2*) cos…

A:

Q: Find all values of x in the interval (0, 27] that satisfy the equation sec2 x + 2 cos² x = 3

A:

Q: Let z = 8(cos 50° + i sin 50°) and w=2(cos 30° + i sin 30°). Express in the form r(cos+ i sin 0):…

A: Here we can use the following formula to find the results eiθ=cos θ+i sinθande-iθ=cos θ-i sinθ

Q: Find the residues of sin(2²) at z = 0 and z = π. (sin z)2

A: To find the residue of sinz2sinz2 at z=0 and z=π Let  fz=sinz2sinz2=sinz2csc2z…

Q: Find / sin(2r) PV -dr R I +4 by invoking Jordan's lemma.

A: Sol

Q: a) By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x – 4 sin°x .…

A:

Q: Prove that v2 cos(20+45°) = cos e-2sin Ocos 0-sin 0, where 0 is measured in degrees.

A: *formula:- cos(A+B) = cosA*cosB - sinA*sinB. sin2A = 2sinA*cosA. cos2A = cos^2(A) - sin^2(A).

Q: 3 ven sin(0) = for <<m << then cos(

A: Topic:- trigonometry

Q: 7 Use the Intermediate Value Theorem and Rolle's Theorem to show that the equation 2 = sin z+1 has a…

A: use the intermediate value theorem and Roll's theorem to show that the eqautionx2=sinx+1has a…

Q: Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

A:

Q: 3. If v = sin- (4) + tan-' (±), find the value of r + y. 4. If z= ear+by. f(ax – by), prove that b…

A:

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

A: Given

Q: Prove that the equation sinx = 0.3 has at least one solution in the interval(o, π/2).

A:

Q: Express f (0) = cos 20 + 4(sin 20)² + 1 as a sum of powers of sin 0.

A:

Q: Solve 2 sin (z) – sin(z) = 1 over the interval (0, 2) O z= O z= 5, O z= ,, 2'6

A:

Q: 2) Find all solution of the equations in the interval [0,2x]. a) 2sin 30+ 12 = 0 b) (cosx- 1)(sin x…

A:

Q: (3 cos t – 1)i + (2 sin t + 3)j,

A: We sketch the curve as

Q: Determine the value of the serie 4∑ ((-1)^n)/(n^2) *cos(nx) at the point x=1

A:

Q: .2 1 2x -1 Prove that : sin .2 dx = 72 1+x 1+x?

A: Solution of given question is given step by step

Q: Find the length of the path over the given interval. (5(0 - sin(0)), 5(1 – cos(0)) ), 0 < 0 < 2n

A:

Q: Determine the concavity of y = 3 + sin x on [0, 2π]

A: The function y=3+sinx on the interval 0,2π. We have to determine the concavity of this function.

Q: 19. For all positive angles less than 360°, if csc(2x +30°) = cos(3y- 15°), the %3D sum of x and y…

A: Given that csc(2x+30°)=cos(3y-15°) It is known that csc(x)=1sinx. So, 1=sin(2x+30°)cos(3y-15°)…

Q: 4. Express in the form a + jb, (i) 2(cos 30° +j sin 30°) (ii) 5(cos 57° -j sin 57°)

A: To write in the form of a+jb

Q: 1. Use Green's Theorem to evaluate [(3ye* -7 sin (3x*))dx + (5x* +2x*y* +8e*-y* )dy, where C is the…

A:

Q: 4. Prove that the identity is true. 1- cost e = sin² 0 1+ cos e

A:

Q: Can the Intermediate Value Theorem be used to prove that the equation 9 2(r + 9) sin*(x) – 4 cos"(x)…

A:

Q: What mathematical result is applied to prove that sin^2(e)+cos^2(0)=1?

A:

Q: e). Prove that Sin3A+sinA 25in2A -COSA

A:

Q: How do you solve this?

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Q: 2. If x = 2 sec 0 and 0<0< T/2, then %3D (a) sin 0 = (b) cos 0 (c) tan 0 =

A:

Q: 4 sin 2t + 2 tan 2t = 0 %3D

A: 4sin2t+2tan2t=0

Q: Prove that (a) Pn (cos 0) = 2F1(-n,n+ 1; 1; sin²0/2).

A:

Q: e sec(3x+2) sin(3x+2) dx Evaluate cos² (3x+2) -3e sec(3x+2) + . O 1 ,sec(3x+2) + C 3 1 ,sec(3x+2) 3…

A:

Q: .2π π 1 -εrocos? θ r dr sinθdθ φdφ x 32 πο X = ?

A:

Q: Prove: sin? xcos?x = - cos(4x). 8.

A: We will use various trigonometric formulas to prove the given identity.

Q: 22-j is 1. -1+jZ If Z = cos 0 + j(1+ sin 0), show that the magnitude of

A:

Q: 7. Prove that: ++) + sin; + e) = v3cose (3) (a) COS

A:

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.