cos + da by using substitution technique where k is a 2 points Compute co(+k), cos r constant. [Hint: cos (A+ B) = cos A cos B # sin Asin B] %3D x cos k - In(cos x) sin k + C x cos k + In(cos x) + C k(x cos k+ In(cos x) sin k) + C x cos k + In(cos x) sin k+ C 29°C Partly s

Q: 2 sin A 1- cos A + sin A is equal to - then 1+ cos A+ sin A If y = 1+ sin A 1 y y O Option 1 O…

A:

Q: sin sin 3x = 2 co 4 sin x cos x - 4 sin x cos x X COS X vith the left-hand side, use a Sum-to- sin…

A: Here we have to verify the idnetity,  sin5x+sin3x4sinxcos3x-4sin3xcosx=2cosx

Q: 57 4. Find all absolute and local extrema for the function f (x) = x-2 cos a on Clearly -TT, %3D 2…

A: objective is to find the local minima and local Maxima.

Q: Use integration by parts to evaluate 2x cos (x) dx -x?cos (x) +c - 2x cos (x) + 2sin(x) +c x?sin (x)…

A:

Q: cos (r+k) Compute de by using substitution technique where k is a cos E constant. [Hint: cos (A+ B)=…

A: Integration

Q: 7) y=Flx)=cos" (x) A.) xCcoskl) =4 Cos? (x) %ax (coscx) =4 cas? (x) (-sin(x). 4 Cos (x)Sin(x) %3D…

A: Explanation of the answer is as follows

Q: Įsin x cos^(3/2) x dx * O -2/5 cos^(5/2) x + C O None of the choices -5/2 cos^(5/2) x + C O -2…

A:

Q: 212 sin(k/n). lim 1. cos(1) + 5/3 2 cos(1) +1/3 +2/3

A:

Q: 5 sin x If f(x) then 2 + cos x 5(1+2 cos (2)) f'(x) = (2+ cos( z))? (2+ cos( x) f'(5) = 0

A:

Q: 1- csc x ... Differentiate: f(x) = sec x f' (x) = csc² a – sin æ ... f' (x) = – sin a – sec? x ...…

A: We have to find derivative

Q: 3 sin a If f(x) –, then 2+ cos x 3+ 6 cos(x) (2+ cos (z))² f'(x) = f'(5) =

A: For part (b) just put 5 in place of x in the expression of part (a).

Q: H.W 1: Prove cos 4x = 1-8 sin² x . cos' x H.W 2: Prove that: sin 2x cos 2x sin x cos x sec x sin ( a…

A: 1) Prove that cos 4x=1-8sin2 x ·cos2 x. Consider the left hand side. cos 4x=1-2sin22x…

Q: n Σ tan(kx) tan ((K+1)x) K=A

A: Given,           ∑k=1ntan(kx)tan(k+1)x

Q: Using appropriate substitution 3. tan’x dx sec5x is equal to -cos°x + cos"x + C tan*x + 6 sec°x + C…

A:

Q: Evaluate S sin“ (x) dx 4 Select one: -cos (x) sin(æ) +(x – sin(2a)) + C None of these 글sin'(2)…

A: ∫sin4x dx = ∫(sin2x)2 dx We have cos 2x = 1-2sin2x2sin2x = 1-cos 2xsin2x=1-cos 2x2

Q: Sin x 10. y = 2+Cos x 3 2+Cos x Ob. (2+Cos x)? Cos x C. (1+Cos x)2 1+2 Cos x d. (2+Cos x)? Oa.…

A:

Q: Sinx e* lim x→0 x- Sinx (b) If x = cos0,y = cosm0;m is an integer greater than unity, prove that %3!…

A:

Q: Choosing between A B or C HW 12

A: We know that,

Q: f(x) = 5 sin²(x) Hint: Use sin2(x) = -(1 – cos(2x))| %3D %3D n = 1 8.

A:

Q: 12. Evaluate ((1– cos x) dx a.) 1- sin x +C b.)x - cos x +C c.) 1- cos x+C d.) x- sin x+C 13.…

A:

Q: 60. Does knowing that 2|xy| x²y? < 4 – 4 cos V|xy| < 2|xy|| tell you anything about 4 – 4 cos V]xy|,…

A: According to the given information, the given fact is:

Q: Ísin^2 (x) cos^2 (x) dx * O 1/8 x -1/32 sin4x + C O 1/8 x - 1/32 sinx + C O 1/8 -1/32 sinx + C O…

A:

Q: cos2x – sin2x cos2x - dr = -F(x)+C. What is Fx)? 19. For cosx – sinx 3 A. (cscr - secr)3 2 2 sinx -…

A:

Q: f(x) = -12sin(x)cos(x) f’(x) = -12cos(2x) f’(π/6) =

A:

Q: n[-5, 7), 1-cos x Find the absolute extremum point (s) of f(x) = e- if any.

A:

Q: (a) Use integration by parts to verify the reduction formula [cos xdx = cos xsm x , n-1 (cos"² xde…

A: Let ux and vx be any two functions. The integration by parts method is used to evaluate the integral…

Q: 3 65 7.Secnario-1: cos" + sin +cos ec 13 5 16 Secnario-2: f(x)= tan x. 1-x² a) Show that 2 tanx =…

A: Given,cos-135+sin-1513+cosec-16516and fx=tan x

Q: (d) r(π/6 + At) - r(π/6) = √3 2 cos At sin Ar-1+(cos Ar i+ At + 2 3√3 2 -sin At 1 3/-)1 2 X

A: We can solve as follows

Q: S sin(1 — х) (2 — cos(1 — x))* dx - C (2-sin(1-x)5 +C A (2-sin(1-x)5 + C - 5. 5 (2-cos(1-x)°+C D B…

A:

Q: 3. Using trigonometric substitution, what is 1 sec-²¹ ( 137 ) + √x²-9 2x² + C A. 1 300² (2) √²-90…

A:

Q: 6. Which of the following is FALSE? 7. f A. (4 cos x-3 sin x) dx = 4 sin x + 3 cos x + C B. f3e³x dx…

A:

Q: 2sin (2x) cos(2x) dx = cos (2x) + C sin (2x) + C 6. the above the above cos (2x) + C 6. sin (2x) + C…

A: We need to evaluate ∫2 sin5(2x) cos(2x) dx                           (1) Let sin(2x) = t On…

Q: (a) Use integration by parts to verify the reduction formula cos"xsin x n–1 Scos" xdx = - [cos" ² x…

A:

Q: 1. 10 – (sec x + 1)(sec x- 2) 18 sin x cos x+ 12 sin x cos x-15 sin x cos x 2. 3 sin x cos x

A:

Q: 4 sin x cos x + 2 sin x - 2 cos x - 1 = 0

A: first factorize the given equation and than split two product equation  detailed solution is given…

Q: 5 sin x If f(x) then 2 + cos z 5(1+2 cos( z)) - cos (x))? f'(x) = f'(5) =| 0

A: Please refer the attached image for complete solution. THANKYOU.

Q: the open interval on which the function is increasing or decreasing. (Enter your answers using…

A: Topic:- function and application of derivatives

Q: ➡pose m and n are constants and m ‡n. Evaluate sin(mx) cos(nx) dx` 1 -cos(m-n)x- -cos(m+n)x] + C n-m…

A:

Q: 3) [~x cos² (x3/2 - 8) dx , A)sin (x/2 - 8) + C 1 = x3/2 – 8 3) 1 B) a32 - 8) + sin 2432 - 8) • C D)…

A:

Q: 18) tan 3x 24) 2sin? 0 3(1-cos 0) 4 25) sin (20)= co cos O 19) cos-x X- cot 26) 4 cos B = 1 + 4sin B…

A:

Q: 1+2 sin x cos x 1-2 cos2 x sin x+cos x (d). sin x-coS x | |

A:

Q: Write cos 3x as a third-degree polynomial in cos æ. [Hint: Write cos 3x as cos (2x + x)] Select one:…

A: Given: cos(3x) = cos ( 2x + x )

Q: Solution :- we have Fla) =5 cas 2x %3D Now di'fferentiate it wot x x d (cos2x) %3D Źx(-2sin2x) %3D…

A:

Q: e2x – (e* cos x)² x2 ´e* sin x and g(x) = (m), x # 0. - f(x) х (a) Show algebraically that f(x) =…

A: We have to show f(x)=g(x) by using Algebraically way:

Q: = sin(7 - by), where = s and y = e-25, Using an appropriate chain rule, determine Let z as O dz 7…

A:

Q: 34 Express cos x + V3 sin x in the form R cos (x-A), where R> 0 and 0<d< Hence find (a) The general…

A: According to the trigonometric formulae we have: cos(A-B)=cos(A)cos(B)+sin(A)sin(B)

Q: y 5)if y =x6- 3x + cos x then a) 360x2-72+ cos x b) 6x5 - 12x3 + sin x c) 120x3-72x + sin x d) 360x2…

A: Since this is a multiple question according to the Bartleby Answering rule, only first question is…

Q: 1- sin(x) A cos(x) +x+C COS 1+ sin(x) B -x+C cos (x): cos(x) -+C cos(x) – x 2cos(x) D 1+ sin(x)

A:

Q: 25. f(x) = e sin x, g(x) e cos x 26. f(x) = 2 cos x + 3 sin x, g(x) = 3 cos x - 2 sin x %3D %3D

A: Linearly independent solution