QuestionTO cos( z+ Da sin(e-2+ In(z)) + C 4 Ob. -4 sin(e-z+ In(z)) + C Oc. --- sin(e-z+ In(z)) + C 4 O d.4 sin(e-2 + In(z)) + C

Q: (e) Inside r 3 sin 0 and outside r = 1+ sin 0

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

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Q: Determine the value of f(z) = e*cos y+ ie*sin y at z = In 4+ Ti/6

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Q: 4. The area which is inside the circle r = 8 cos e and outside the circle r = 2 cos 8.

A: Introduction: In polar coordinate, the equation of a circle centered at the origin with radius a…

Q: (-n *) Prove sin? x – sinx cosx – 2 cos? x =0 in п, 2 has five root's Hint. Intermediate value…

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Q: (p² –1)cos[cosh (In r)]dr

A: In this question, we need to find the integral.

Q: Determine the value of f(z)=e*cos y+ ie*sin y at z = In 4+ Ti/6.

A: For a complex number, z=x+iy , x is the real part and y is the imaginary part .

Q: n the der natwe of Sin (x )= Sin Cx-cos (rE)) to CoS

A: Definition: Differentiation is the action of computing a derivative. The derivative of a function y…

Q: Verify the identity: sin(x - y)/(cos x cos y) + sin(y - z)/(cos y cos z) + sin(z - x)/ (cos z cos x…

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Q: sin (+) can be expanded to: π TT O sin COS sin sin 4 7 TT O sin sin COS cos 4 T Osin COS + cos sin…

A: Solved below.

Q: The rose - Firnt patal is given by the equation Select one: OT= 5 sin 80 where 0 E [0, 27]. OT=5 cos…

A: Given:          From the above graph the rose has 8 petals.    The polar equation r = b.coskθ , 0 ≤…

Q: 4. Verify the identity sin(z+y) %3D COB E COS y tan z+ tan y

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: Evaluate the integral. sin COs 503 502 502 sin 50 1. cos d0 3D 502 502

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Q: 2. Extend the identity cos(ax)-cos?x-sin'x for xE PR to the identity cas (a2)- Cos s 2-sinz for & €…

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Q: Prove the left side equal to right side in the following: s2 (eice = (sin at + at cos ar] 1 L-1 (s²…

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

A: Sol

Q: Hiw ABy using Euler's formula prove That: sin(-2) = cosz CamScanner - n pal O Cos(そ2T)cosz Sin? Z+…

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Q: Find 1+sin -cos I COS In | sin - z+cos In In 1+tan +C +C +C +C

A: We can evaluate the given integral by using the substitution u = tan (x/2).

Q: In Problems 28–44, establish each identity.

A: Trigonometric identities are given, we have to prove the identities. Note: we are answered with 3…

Q: Evaluate et sin z cos z dr I COS using Simpson rule with h 20

A: Simpson rule  ∫abf(x)dx=h3f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(x4)+⋯+4f(xn-3)+2f(xn-2)+4f(xn-1)+f(xn) Where…

Q: For sin(u/2), cos(u/2), and tan(u/2) given cos(u)=-sqrt2/3 and sin(u)>0 I got…

A: Given  cos(u)=−23sin(u)>0

Q: 0° S (c) Prove that: 2cos 20. cose 2 + 2 tan0. sin0 = %3D cos?e – sin? e cose o AEGW is drawn.

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Q: -cos x + sin x in the form r sin (x + a), where r> 0, is: e A. 2 sin x+ -sin |x+ 4 B 57 2 sin x+ 4 2…

A: We will find out the required expression.

Q: Prove: sin? x 2 cos“ = cos 2-2cos x

A: We will use basic properties of trigonometric ratios

Q: What is the general solution of sin z sin ydx + cos rcosydy 0? %3D

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Q: Find the exact values of sin and cos for sin e= on the interval 0° s es 90°. 2 sin 0.1691, cos…

A: We know that,  cosθ=1-sin2θ         cosθ>0 in 0°≤θ≤90°        ⋯⋯1sinθ2=1-cosθ2…

Q: If sinh x =tan t, 0<t<3/2 , then tanh x = sin t. Select one: O True O False

A: We have been given  sinh x= tan t for 0&lt;t&lt;3/2

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

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Q: =/4 sin z 23)/" dr cosr

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

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: An appropriate trigonometric substitution 1 -dx is V4 – x² for x = 2 tan(8) for 0 E (-5,5) а. b. x =…

A: The given integral is: ∫14-x2dx

Q: ered # tion Bi Q) choose one only 1. If (x + y)² = x² + y² prove that = - dx 2. If y = sin³ () cos³…

A: To find the differentiation of given functions.

Q: The integartion of [sin(sinØ)]Ø cos dø Is: cos(sin0)+C -sin(cos Ø) + C O -sin(sinØ) + C O -cos(sinØ)…

A:

Q: 8. Evaluate (a) /sin z cos" z dr (b) / (ln z)* dz. You may use /In z dz = z ln z - z+c.

A: Let's find.

Q: 7. Prove: (a) sin iz = i sinh z. (b) | cos z|? = cos² x + sinh° y where, z = x + iy. COS

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Q: 2) If z = cos 0 +isin 0 show that 1 = 2 cos 0 a) z+-D 1 b) z" + 2 cos no %3D

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Q: Assume that x, y ER and z = x + iy E C and answer the followings: 1. Evaluate sin(i) =?, cos(i) =? ,…

A: Since the questions contains many subparts as per the guidelines I am answering the first three…

Q: TO For x such that 0 < x<, the expression 2. V1-cosx V1- sin'x COS"X is equivalent to: sin x COS X

A: I am solving this in step 2

Q: a Show that (sin(m + n)x + sin(m – n)x) b Hence, without using the product rule, differentiate sin…

A: We will find out the required values.

Q: 23-Frove that. Cos3e - Cos'e- 3 Cos e Sin'e

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

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Q: Find z where z = sin (æ²) cos (4²) COS

A: The given function is z=sinx2 cosy2.

Q: Which of the following is equivalent to [sin(-x) + cos(-x)]? 1 - 2sinxcosx O 1 O 1+ 2sinxcosx O…

A: Use Trigonometric identities and simplify.

Q: 5. Integrate the following and show all of your work: sin“ r cos r dr

A: we have to integrate the following

Q: What is the general solution of sin 0-2rcos²0) dr + rcos0 (2rsind + 1) de = 0 ? %3D O sin 0 rcos²0…

A: Given differential equation is: sinθ−2rcos2θdr+rcosθ2rsinθ+1dθ=0

Q: a sin a + In v ) da + tan adv = 0 Cos a

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Q: Verify the identity. sin (e + n) = -sin e A) sin (e+x) = cos Osin e- cosa sin a = cos Osin e--0 =…

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Q: 4) Sin W = %3D Cos N = W. Tan W = %3D

A: Solution: The objective is to find the required values