1. Show that | sin x cos3 x dx = sin® x sin x +C = - 8. cos*x, cosx cosx +C 3

Q: 12 and x terminates in 13 nd sin 2x, cos 2x, and tan 2x if sin x= sin 2x cos 2x %3D tan 2x %3D II

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Q: 18. Evaluate ſe3 cos 2x sin 2x dx 1,3 cos 2x + C c.e3cos 2x + C B. -e3 cos 2x + C e3 cos 2x D. 6 sin…

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Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

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Q: Evaluate [(1 +x-3 + sin4x)dx -2 cos4x X - + c 4 0x-- cos4x + C cos4x O 2x- 4 0 4x-두-5t +c cos5x + c…

A: As we know that the integration of : ∫fx±gxdx=∫fxdx±∫gxdx ∫xndx=xn+1n+1+c ∫sinxdx=-cosx+c

Q: Q1/ Show that 3(sinx-cosx)*+6(sinx + cosx)²+4 (sinºx+cos°x) = 13

A: Note: We are entitled to solve only one question at a time. To Show:…

Q: O yotan' (x'+3x-s)+ sin (x²s 2x -1)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The f sin 2x cos 2x dx is 1+3 cos 4x 1 sin²4x + C 24 1 In|1 + 3 cos 4x| + C 12 {A} {B} {C} - In|1 +…

A: To find the value of the given integral ∫sin2xcos2x1+3cos4xdx using substitution

Q: 5. Show that cos (sin 2x) + sin (cos-1 2x) = (V2-2x)(VZ+2x) -

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Q: 11. Evaluate the integral: tan 2x dx A. -In| sec 21| + C -sec² 2x + C С. -In| cos 24| + C D. 2 sec…

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Q: 7. Show that sin E + x) = G+x): = -cosx.

A: Introduction :

Q: verify the results  sin 4x = 8 cos3 x sin x − 4 cos x sin x  tan2 x =1−cos 2x/1+cos 2x

A: To prove: sin 4x = 8 cos3 x sin x − 4 cos x sin x Proof: Since sin2x = 2sinxcosx sin2(2x) =…

Q: tan(2x) O 1+ cos(4x) sin(4x) O cos(4x) – 1 sin(4x) O 1- cos(2x) sin(2a) sin(4x) 1+ cos(4x)

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: 2. 5. xcos x (sin'x - 2sin'x + sin°x)(cosx)

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Q: What values of x in the interval [0,2pi] satisfy 2 + 2cos(x) - sin2 (x) = 0

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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…

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Q: 1. fcosax tan(sin ax)dx - In |cos(sin ax)|+ c ans : or In |sec(sin ax)| + c 2. Ssin(cos.x)·sin x dx…

A: Here we use the other formulas with the given one and also use substitution.

Q: Evaluate sin 2x sin 4.xdx 2 b. sin 3 2x + C 3 1 a. sin ' 2x+C 3 c. cos' 2x+C 1 с. 3 d. -cos 2x +С 2

A: To evaluate the given integral: ∫sin 2x sin 4x dx

Q: 6. Evaluate A sin³ x cos4 x dx.

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Q: Evaluate: 8 sin xcos xcos 2.xdx -cos 2x- 1 cos 2x +C 10 8 cos 2x--cos 2x +C С. A. 14 1 -cos 2x 10 1…

A: Integration is generally used to calculate area under the curve. When function definition changes…

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

A: We will use L'Hopital rule

Q: 16. If 2 sin 2x s 3 cos2x and 0s 2x then x=

A: Given : if 2sin2x = 3cos2x and 0≤2x≤π2 . then we have to find the value of x.

Q: Evaluate cos x + 2 cos³ x + 1 dx cos' x cos4 x 7 +x + c 2 sin7 x sint x +x + c cos x +x + c 3. cos X…

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Q: tan 2x – 1 dx. 5 tan 2x + 5 Q5: Determine 1 In |sin 2x + cos 2x| + C 10 A 1 В In |sin x + cos x| +C…

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Q: Compute 2° sin(x" + 2) dæ. O -7 cos(x" + 2) + C O 1 cos(x² + 2) + C O - cos(2" + 2) +C 1 cos(2" + 2)…

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Q: Show that cos 3x = 3x has a solution in the interval [0, 1]. Hint: Show that f(x) = 3x – cos 3x has…

A: solution:-f(x)=3x-cos3xapplying intermediate value theoremintermediate value theorem states that if…

Q: 1. Solve the DE tan x sin y v + ( 3tan X -2 cos y) sec'x=0

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Q: If x= cos n + cos 2n and y=sin n + sin 2n show that  2xy= sin 2n+2sin 3n+sin 4n

A: See the attachment

Q: Evaluate cos (x (x2 – 2x + 1) (2x - 2) sin (x 2 - 2x +1) (2 – 2x) sin (x? – 2x + 1) O (2x 2) cos (x-…

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Q: Find sin(2x), cos(2x), and tan(2x) from the given tan(x) = -, cos(x) > 0 %3D sin(2x) = %3D cos(2x) =…

A: Given: tanx=-16,   cosx>0 sin2x can be calculated as, sin2x=2tanx1+tan2x          =2×-161+-162…

Q: Suppose: sin(x) = -0.1 cos(y) = 0.5 tan(z) = -4.3 Then, sin(-r) =| 0.1 cos(-y) = 0.5 tan(-2) = 4.3…

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Q: 1 os( 1 (sin(7z))* =| x)+ cos( x)

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Q: 8. 5 cos²x - 3tan x COS X dx

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Q: 4. Prove that cos(sin¬1 x) = /1 – x².

A: cos(sin-1x)=1-x2⇒sin-1x=cos-1(1-x2)Let y=sin-1x                               (1) ⇒siny=x…

Q: d. Show that sin 8x + sin 4x cos8x-cos4x = -cot(2x)

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Q: (i) Prove that sec 3x(sin 3x-2sin' 3x)= tan 3xcos 6x. (ii) Hence find, for 0s.xs, the values of x in…

A: Trigonometric equation

Q: 17. If 4 sin x+3 0 on 0 sx < 211, then x=

A: We have to find x if 4 sin x+3=0 on 0≤x≤2π. Solving the given trigonometric equation, 4 sin x+3=04…

Q: Evaluate / 7x cos(x)dx 07 (x sin(x) + cos(x)) + c Oc – 7 (x sin(x) + cos(x)) - 07 sin(x) + 7 x…

A: The solution for given problem is :

Q: Compute (sin (x)) dx cos'x 3 sin' x cos x O Not listed here 3 sin? x 3 sin x cos x

A: Given query is to find the derivative of the expression.

Q: Find , if da y = 3x cos4x 12x* sin4x – 10x cos4x None -2x4sin4x – 12x° cos4x -12x4 sin4x + 12x°…

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Q: [² 11. [(2 sinx+cos.x) dx 9. 13. 15. x¹/3 19. 21. 3 x2/3 - dx 17. [(3 cos x - 2) dx [(5x- 2²/1) dx…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Evaluate: | tan(4x + 3)dx i -In |cos (4x+3)|+C A COS 4 В 4 - In |sin (4x + 3)|+C In |csc (4x+3)|+C D…

A: Given: ∫tan(4x+3)dx =∫sin(4x+3)cos(4x+3)dx Substitute :…

Q: The suitable substitution to evaluate | sin 4(x+2) dx is None (1- cos8(x +2)] [1- cos4(x + 2)]…

A: Given that: ∫sin24(x+2)dx

Q: 1. Solve the DE: tan xsin y y'+(3 tan x-2 cos y) secx= 0

A: Given tanxsinyy'+3tanx-2cosysec2x =0 tanxsinydydx+3tanx-2cosysec2x =0 3tanx-2cosysec2xdx+tanxsinydy…

Q: 17. Evaluate f-3x cos 2x dx a. --cos 2x - 3xsin 2x + C b. -cos 2x -sin 2x + C C. -cos 2x -³x sin 3x…

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Q: 7/3 In(tan x) dx T/4 sin x cos x dx

A: It is simple substitute method of integration

Q: Show that n/2 sin x dx sin x + coS X %3D 4

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Q: Show that 4 sin x cos 2x + 3 = 8 cos %3D x.

A: We will use the formula of cos 2x and other formulas of trigonometry to prove left hand side is…

Q: Suppose f (x) =cos( 2– 3x). Evaluate: )dx A - 3sin(3x – 2) +C ® -;sin(3x – 2) + C sin(3x – 2) + C D…

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Q: 04.) Show that y = (sin x +cos x) sec x = sec² x

A: Given inequality does not equal. See the attachment