T/2 TT/6 sin x 2 1.)Prove that

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

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Q: Prove that: 1. Z, Z2 =r¡r2[cos(0, + 02) + i sin(0, + 02)]

A: According to our company policy we can only answer first question and rest of questions can be…

Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: Find all angles between 0 and 2n satisfying the condition V2 COS T = Separate your answers with…

A:

Q: Show there is a root to the function f(z) = 9 sin z – 3x + 2 on the interval (3, 1). est tenth if…

A: Here we have, f(x)=9sinx-3x+2 ............. (1)  To prove:- The root of the function f(x)=9sinx-3x+2…

Q: Prove that J5/2(x) = 2 TCX CScanned with CamScanner 3-x² 2 sin x - 3 COS X

A: Use the given information.

Q: 1. If y= tan x, prove that y"= 2(y² +1)(3y² +1).

A:

Q: Let h(z) tan(5x + 5). Then h' (2) is and h'' (2) is

A:

Q: d Q 3. Prove that tanx dx sec?x. =

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Q: If u(t) = (sin(4t), cos(2t), t) and v(t) = (t, cos(2t), sin(4t)), use Formula 4 of this theorem to…

A: Find u(t) . v(t) first then differentiate with respect to “t”.

Q: 1. If y= tan x, prove that y``= 2(y² +1)(3y² +1).

A:

Q: Use the substitution formula to evaluate the integral. (1 + cos 3t) 2 sin 5t dt 15 15

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Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

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Q: •2n Let a and b be distinct nonnegative integer. Prove that Sa sinax cos bx dx = 0 %3D

A:

Q: sin (21 + 1) dt J cos² (21 + 1)

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 10. Prove that T/2 75/2. sin e cos (cos a cosec 0) de 10 T 2 (1-cos a).

A:

Q: 9. Let r = 3 sin tî + 3 cos tj + 4tk. Calculate N

A: Given r(t) To find N(t)------ unit tangent vector

Q: 2 = using the relation r= VT show that sin x %3D EX II

A:

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

A: The given problem is to prove the following complex identity. (cos n/5 θ +i sin 2n/10 θ)+1/einθ =…

Q: Find дх (дхду) 6,e at the point(7,), where g(x,y) = cos(y) [sen(x) + xy].

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Q: 2t Show that f/² sin tdt ≥ 7. (Hint: sin t ≥ ㅠ over [0, 1].)

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: The f xcos x² 1-sin x2 dx is

A: Given :

Q: dt, evaluate F(0) and F'(0). Given F(x) = Ju- 5. %3D J1+sin(2x) 1+ et-1

A: We have to find out

Q: Let - (sin x cos y, COS I sin y, In). Compute div i

A:

Q: 7/2 79. Prove that 0< sin x dx < Ja/4

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Q: Find the residue of f(z) = (1 – 26) sin(1/2).

A:

Q: 2-If w(x, t) = Sin(x - + 3t) + Cos(2x+ 6t), prove that wtt = 9wxx %3D %3D

A:

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

Q: Evaluate the integral. 1/2 cos(t) dt 1 + sin?(t)

A:

Q: b) verify the functions sin(3x) and cos(3x) are linear dependent or Linear independent.

A: Hence linear independent

Q: show that1) d/dz [cosz] = -sin z

A:

Q: If u =x² cos y +ye», where x =s+2t and y= st, prove that ди 2- Əs ди 3 (s— 21) (х' siny — хуе" —…

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Q: - Using Euler's equation, show that- : z fain (K 0)} - z sin Ø z2 – 2zCos Ø +1

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Q: A. Ifw= sin(x+bt)+cos(2x+ 2bt) . Prove that ôx? B. If f = x*y* + 2y sinx + x² lny then show that fxy…

A: A)

Q: (a) If u(x, y) = cos-1*" + y* ) x² + y? = COS then prove that ди du + y = -2cotu

A: Given: ux,y=cos-1x4+y4x2+y2

Q: - Show that u(x,t) e-a't[A sin(2x) + B cos(Ax)] satisfies the PDE uz = a?uxx for arbitrary A, B and…

A:

Q: إعادة تعيين Q5. Let a and b be distinct nonnegative integer. Prove that sinax cos bx dx = 0 إلغاء

A: We will find the value of integration.  We know the formula of  2sinA cos B = sin(A+B) + sin(A-B).

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

A: We have to find derivative

Q: Q6:-Prove that: y" = 1 y =csc(tan"" ) if

A:

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

A:

Q: Find all values of in the interval 0, 2 such that sin x = sin 2x

A: To find all values in the interval for the function

Q: a. Show that W[5, sin2 t, cos(2t)] = 0 for all t by directly evaluating the Wrosnkian.

A:

Q: Prove that d/dz sin(z) = cos(z) using Cauchy-Riemann equations

A: Cauchy-Riemann Equation- If f(z)=u(x, y)+i v(x,  y) is analytic, then In particular, These…

Q: 1. If y= tan x, prove that y= 2(y´ +1)(3y² +1).

A: Use the following differentiations as, ddx(tanx)=sec2(x)ddx(sec(x))=sec(x)tanx Now, differentiating…

Q: Prove that: Z,Z2 =r,r2[cos(0, + 02) + i sin(0, + 02)] 1.

A: NOTE- As we are allowed to answer one question in one session so, i have answered first one for you.…

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

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.