| sin? x cos x dx The set-up would include . u = sin x and -du = cos xdx cos x and du sin xdx Ou = COs x and -du sin xdx sin x and du = cos xdx

Q: If sin(x + y) – sin(x – y) = 2f(x) sin y, then f(x) is equal to C. tan x D. cos? x A. sin c B. cos x

A: Trigonometric functions are also known as circular functions. They can be defined as the functions…

Q: sec? a tan zdz Evaluate +C

A:

Q: If S (x) = - sin(x), then f (11) (x) is equal to – sin(x) B B -cos(x) CosX sin (x) D O cos(x) A,

A:

Q: Four equations are provided below. Which equation follows from the Power Rule? I. (P)' = pr P 1…

A: Answer is option (a)  Because only equation 3rd follows the power rule .

Q: | 12sin z cos zý3 sin? z + e® dz

A:

Q: تفاضل وتكامل )2( نظري Stan?x dx = Select one: a. sin x-x+ C on b. COS X-X+C C. sec x +x+c d. tan x -…

A:

Q: Given f(x,y,z) = cos(4xy) + sin(4z). Find f,(8,9,0)

A: We can find the answer as below.

Q: If sin x - x sin x = -y cosx , then (y - 1) sin x = ? da C- x sip C+x sitft (B C - x COSX C+x COs

A:

Q: dy ? If sin(x + y) = xy, what is the expression for dx cos(x + y) – Y | A х — 1 cos(x + y) – Y B x –…

A:

Q: For y = sin?x + cos²x, y' = (A) 2 sin x - 2 cos x (B) 4 sin x cos x c) o D) None of the given…

A: We will use chain rule of derivative

Q: y=sin x sec X , then y' = A O cos? x- sin? x B O sec x -csc x 1° D O

A: To find : y'

Q: If f(x,y)=log, (cos²(e* ) +si f(x,y) is ây ôx + sin(x+ y) then %3D

A: Given that: fx,y=logecos2ex2+sinx+y To determine ∂∂y∂∂xfx,y

Q: If f cos xdx = A +B sin x + Csin²x+ Dsin³x+ Esin*x+ Fsin5x, what is , 2 ) and ( - 2,5). the value of…

A: Given: ∫cos5xdx=A+Bsinx+Csin2x+Dsin3x+Esin4x+Fsin5x.

Q: If sin(x + y) – sin(x – y) = 2f(x) sin y, then f(x) is equal to C. tan x D. cos? x A. sin c В. cos x

A: Given; Sin(x+y)-Sin(x-y)=2f(x)Siny

Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find f;(5,5,0).

A:

Q: If sin(x +y) = xy, what is the correct expression for -? dx cos(x + y) – y (A х-1 cos(x + y) – y (B…

A:

Q: If f (x) = – sin(x), then f (11) (x) is equal to A -sin(x) B - cos(x) © sin(x) D D cos(x) B

A:

Q: W (1, sin x, cos x) =

A: Use formula for the wronskian is determinent form.

Q: =? |c0,1,1) What is the x* In(=) +sin xyz +ev = 0 y O a. -2/e O b. 0 O c. -1 d. O e. e/2

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Q: 20. sin? x cos? x dx

A:

Q: Find the root of f(x) = e −x (3.2 sin(x) − 0.5 cos(x)) on the interval [3, 4] up to 1 d.p.

A: Consider finding the root of f(x) = e-x(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

Q: 1. If we are trying to evaluate thef esinx cos x dx, which substitution would be most helpful? А. и…

A: Select the correct option?

Q: The following is equivalent to the choices below except | (tan (x)+ 1) dx 1 dx cos? (x) sec (x) dx…

A: Please refer the attached image for complete solution. THANK YOU.

Q: (x cos + y sin?)y – (vsin? -x cos?)* х — х COS = 0 Ans: xy cos = c (Lucknow, 1997; Kanpur, 1996)

A:

Q: Which of the following is not equivalent to sin' ædx sin" zdz 1 4 x cos a + 5 cos z + C - cos a +…

A:

Q: If f cos xdx = A + B sin x + Csin²x+ Dsin³x+ E sin*x+ Fsin5x, what is the value of A + B + CD + E +…

A: Consider ∫cos5x dx =∫cos4x cos x dx =∫(cos2x)2 cos x dx=∫(1-sin2x)2cos x dx…

Q: If f x sin x cos x dx =xsin?x + Ax + B sin 2x + C, what is the value of A + B? ` 1 1 8. 1 4

A: Solve by parts method of integration.

Q: Using an appropriate substitution, f sin (x)cos (x)dx is equal to: sin'x sin +C cosy cos'x 王C 11…

A:

Q: Given f(x,y,z) = cos(5xy) + sin(4z). Find f,(6,6,0). %3D

A: Finding the derivative of f w.r.t z, treating x and y as constants

Q: S sin?x cos³x dx i sin*x -sin*x + c i sin*x +sin°x + C O A B -sin'x -sin'x + d

A: The given integral is ∫sin3xcos3x dx We evaluate the integral using proper substitution. At first we…

Q: 9. By the 3rd order Maclaurin's theorem, we have sin x = f(x) – cos ex. Then f(x) = a) x? b) -x? c)…

A:

Q: S tan?x secs x dx 1 х + Ос none of the choices 1 -sec"x + sec*x + C + C O A B.

A:

Q: If z = x2 + y? x = e' cos(s) and et sin(s y = ), then

A: ∂z∂s=∂z∂x∂x∂s+∂z∂y∂y∂s Lets find out each derivative z=x2+y2∂z∂x =2xx=etcos(s) ∂x∂s=et…

Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find f:(5,5,0).

A: This question is based on Partial derivatives.

Q: If S e2 stn x u dx =;e? stnx + C, what is u? {C} sec x {D} cos x {A } 2 cos x {B}2 sin x

A:

Q: If f(x, y)= cos(x +y), then- (+: O a. - sin (x + y) O b. - cos(x+ y) COS O c. cos(x+ y) O d. sin (x…

A:

Q: If f (x) = eª sin x, then f' (x) A) et cos X B -et cos x c) e" (sin x + cos a) D) e" (sin x – cos x)…

A: We have to find the option

Q: Evaluate: [Vx+ sin/X d. A 2x+ cos/x + C 2 (B) x- 2cos/x + C 2х- cos/x + C 2 D x+2cos/x+C E None of…

A:

Q: Differentiate: h(x) = ... cot x -e h'(x) = csc2 x ... A e" (cot a + csc? x) cot² x ... h'(x) =' e"…

A:

Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find f,(8,2,0). Answer:

A:

Q: Which of the following is equivalent to: (e-2'e-t cosh t dt 2 L [cos h t] L [e* cos ht] O A.) B.)…

A:

Q: S sin x (cos x)ådx (cos x)ž + C none of the choices (cos x)Z + (sin x)ž + C O A B.

A:

Q: If f(x, y) = e'n(x sin()), then which of the following combination is correct O fx(x,y) = 0 fy(x.y)…

A:

Q: When J x°cos (x-)dx is evaluated using IBP, the value of J v du is? A - cos (x2) B none of the…

A:

Q: S sin? x dx Evaluate 1+cos x

A: ∫sin2x1+cosxdx

Q: Using an appropriate substitution, S sin (x)cos®(x)dx is equal to: sin°x sinx + C 11 cosx cos x + C…

A:

Q: Which of the following statements is true? @ Soue(x*) dr= - coa(x) +c x²+2 - dx =x+ tan(x) +C x²+1…

A:

Q: If f(x, y) = e“ sin(4y) then: 4 sin (4) 4 cos( 4) V f( – 1, 1) . el el

A:

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.