2. lim /1 + cos(п сос х).

Q: 7. Prove that: (3) (a) (4) (b) sin20 cos20-1 in (-0) + cos (- 0) = cost -cote =

A:

Q: Determine and of y = (5r - })(cos z + In z

A: Consider y=5x2+32sin x+ln x. Calculate: dydx=y'. Apply product rule of derivative:…

Q: - 1, z = cos-

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Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

Q: Find sin 2x, cos 2x, and tan 2x if tanx= and x terminates in guadrant III. 3

A: To find the value of sin (2 x), cos (2 x), and tan (2 x).

Q: In(cos ax) ? limx-0 In(cos bx)

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Q: 1-[t2 cos at

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Q: Q3-Prove that (cos303cos³ 0-3cos 0 sin? 0)

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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: 1- CoS T lim 30 r In(1+ z) is

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Q: If sin u  = 3/ 5 and sin v = 4/5  and that u and v  are  between  0 and π/2,   evaluate :     cos (…

A: given: sinu=35 sinv=45 and u and v are between 0 and π2. we have to evaluate cos(u-v)

Q: 12 "2 If Y= \n(Sinae), Prove y =y=- ノ

A: Here, the given function is: y=ln(sin x) So, y'=1sin x(cos x)=tanxy''=ddx(y')=ddx(tan x)=sec2x

Q: 39. Does not exist; cos e – 2 lim 00- cos e – 2 lim 00+ and

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Q: [5] Determine the y(2021) of y=cos²

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Q: 2 cos(5x) – 5 x² – 2 sin(3x) – x2 – 3x - lim - - (Write your answer in the given box)

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Q: 82. Show that cos at cos bt %3D In

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Q: 3. Show that cos 30 = cos 0 – 3 cos 0. [Hint: Apply De Moivre's Theorem.] |

A: Given: verify that cos3θ=cos3θ-3cosθ according to given hint theorem cosx+isinxn=cosnx+isinnx

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

A:

Q: Prove | cosz |2 = cos²x+ sinh²y.

A: To Prove: cos z2=cos2x+sinh2y

Q: 8 and x terminates in guadrant III. 15 Find sin 2x, cos 2x, and tan 2x if tanx= sin 2x %3D cos 2x…

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Q: - IF z = tan2 -1 y Show that x- ây

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Q: In(1+ Vsin²x) lima→0 1 – cos x

A: Given,limx→0ln1+sin2x31-cosx

Q: (a) Evaluate by parts: |x cos4xdx

A: In this question we have to find solution by using Integration by parts.

Q: ,2 - 1 If z = cis 0, show that i tan 0. 22 +1

A: this is complex analysis question and also very lengthy questions so I can do it in advanced…

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

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Q: 15 Find sin 2x, cos 2x, and tan 2x if sinx and x terminates in guadrant III. 17

A: Given that: sinx=−1517 To find: sin2x, cos2x, tan2x

Q: 3x)=てメ+cosス そし-て)- -4-cosいて) そしね)、ずした) ):-Smいて)=20348 Kntl = Kn - ぐし) 0.9651+2.0 348 32 Satisfied…

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Q: 1-cos 5x cOS lim 6x

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Q: 1 Find sin 2.x, cos 2x, and tan 2x if and x terminates in guadrant IV. 10 cosx=

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Q: .If z = e-(sin x + cos y), show that a²z a2z az ax2 ду? at

A: Given - z = e^-t( sinx + cosy)

Q: Find y' (y prime) and y" (double prime)y = cos(x2)

A: To determine the expressions for the first and second derivatives of the given composite function

Q: (5) Use the Intermediate Value Theorem to prove that xe* = cos(x) has a solution.

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Q: 4 Find sin 2x, cos 2x, and tan 2x if cosx= and x terminates in guadrant III.

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

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Q: 12. Write an éxpression that gives all sölutions to the equation. COS X - SIn x 3= 2.

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Q: 4/ Prove that: " cos bx dx = (bsinbx +a cos bx]+c

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Q: Find   cos(u/2)   if   sec u=7.519

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Q: In(]æ| – 1) lim %3D (cos(x))=

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Q: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 01 + tan 02 + tan 03 + ... + tan 0,} =…

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Q: In AXY Z, the mZY = 90°.XY = 19 and XZ = 22. What is cos X? ООО О

A: Given,

Q: find y prime and y double primey=cos(x^2)

A: To apply chain rule and product rule to find the first and second derivatives of a composite…

Q: 2 Verify the identity 4cos x (20 points) 2 2 2 4sin x cos²x + 4sin²x − 4sin³x = 4cos²x.

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Q: Find sin 2x, cos 2x, and tan 2x if tanx=-. and x terminates in guadrant IV 3

A: sin 2x= 2 sin x cos x cos 2x=1-2sin2x tan 2x=(sin 2x)/(cos 2x)

Q: Prove that 2cos^x_1=cos2x

A: In this question we have to prove 2cos2x-1=cos2x

Q: 9 If f(0) = cos 0 c • cos 02· cos 03. ... cos On f'(0) Show, {tan 01 + tan 02 + tan 03 + ....+ tan…

A: We have fθ=cosθ1·cosθ2·cosθ3....cosθn                 ....(1) Now, we have a formula…

Q: When r^2 = x^2 + y^2, we have x = rcos theta and y = rsin theta, and  When r^2 = y^2 + z^2, we have…

A: Consider the following: When r2=x2+y2 , then x=rcosθ  and y= rsinθ, When r2=y2+z2 , then y=rcosθ and…

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

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Q: 2. Prove that cos30 = (4cos'e - 3cos0) and sin30 = (3sine – 4sin e) using De Moivre's Theorem. %3D…

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Polynomials

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