Evaluate L{ sin(t – T) cos t dr - 7) castdr}|

Q: If f(x) = 6 sin x + 9 cos a, then f'(x) =

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Q: Use the Fundamental Theorem of Calculus to find (2 + cos x) dx.

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Q: -T/4 sin x 1+cos²x

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Q: Q.2: Evaluate: cos³ x I = = =dx sinx Hint: Sin’x+ Cos'x =1

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Q: If f(x) = cos a- 5 tanx, then %3D f'(x) = %3D f'(5) =

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Q: Evaluate cos zV1+ cos². dædy

A: Given double integral is                    T=∫01∫arcsinyπ2 cosx1+cos2x dxdy ⋯⋯⋯⋯⋯⋯ (1)

Q: Using (11) and (12): 1 dx 1+ cos x tan +c

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Q: 5. Use substitution to find S sin1º0 cos 0 d0.

A: We will find the integration.

Q: Evaluate So sin(x) dx 1+sin(x) 2 Select one: O 1+ 2 2 -1-5 -1+5 2 2

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Q: Evaluate: sin rv1- 4 cos² x dx. /9 – (In r)² Evaluate: dr.

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Q: D[Expf-3x] Cos(nt], {x,2},t]

A: Correct option is D

Q: 9. dt + 을 = COS t + Answer: s = sin t + 을..

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Q: Rewrite – 4 sin(x) – 5 cos(x) as A sin(x + ø) A = $ =

A: Given the trigonometry function

Q: eln sinx If z = + tan-1x y cosx Find: əz а. əx əz b. ду

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Q: Verify the identity. sin(x + y) – sin (x - y) = 2cos.xsiny

A: To verify the identity, sinx+y-sinx-y=2cosxsiny

Q: Ex2: Use the identities 4 and 5 to prove that: cos(x- y)-cos(x+y) (a) sin x sin y = 2

A: Formula used -  cos(A-B) = cosA cosB + sinA sinB  cos (A+B) = cosA cosB - sinA sinB

Q: Find the W (sinx,cosx , sec x).

A:

Q: Assume sin(t) = -12 where π < t <3. Compute the following: csc (-t) = cos(t + 2) = tan(t) =

A: We have given  Sint = -1/12 , where π&lt;t&lt;3π/2  Compute  1) cosec(-t)  2) cos(t+π/2)  3)…

Q: 4 cos ' (sin (ax t)

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Q: Evaluate ! d(cos x – x)

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Q: If f(x) = sin?x, then f"(x) = %3D A 2cos2x B cos2x -sin2x D -4sin2x

A: Given, f(x) = sin2x For the given function , applying chain rule ,  First differentiate it as { xn ,…

Q: D[Expl-3x] Cos(nt], {x,2},t]

A: Correct option is D

Q: Verify the identity: tan2 t/sec t = sec t - cos t

A: Given : tan2tsect  = sect - cost

Q: 2 f(t) = ( tv4t2 + 1, sin(t) cos² (t), t2 + 1

A: As you ask parts b and c. in part b we need to find the equation of the tangent line to the curve at…

Q: Evaluate si (z* - tan(z) cos(z) ) dx 2-1

A: To find the integral: ∫11x2-tanxcosxx3-1dx

Q: Evaluate in x cos x dx. .3 I COS" T

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Q: (3 cos t – 1)i + (2 sin t + 3)j,

A: We sketch the curve as

Q: Assume cos(t) = - where <t <a. Compute the following %3D cos(-t) = sin(t) = sin(-t) =U sin(-t) +…

A: topic - trigonometric ratios sin(-x)=-sin(x) cos(-x)=cos(x) sin2(x)+cox2(x)=1

Q: Determine f(x) so that cos(In x) f(x) dx = sin(In²x) + C

A: Option B

Q: If f(x) = 6 sinx + 6 cos a, then %3D f'(x) = %3D f'(4) = %3D

A: Simply take the derivative using standard derivative forms.

Q: Evaluate f(t) = cos?(t) = COS COS L{f(t)} %3D

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Q: Evaluate sin z -dx /4 - coS I

A: Use the substitution method and first simplify the integration than integrate.

Q: (2 cos t, 2 sin t, t), where 0 <t < .

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Q: Let r(t) = (sin 3r, cos 3r, /īt), Find T(t) and N(t)

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Q: 2Tt Prove that a" sinax cos bx dx = 0 0.

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Q: Verify the identity: cos t cot t = (1 - sin2 t)/sin t

A: We have identity is  cos t cot t=1-sin2tsin t LHS=cos t cot t RHS=1-sin2tsin t…

Q: Cos X 2)

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Q: Let f(æ) = (7 sin a + 4 cos a)tan-e f'(x) -

A: We can find the derivative using product rule as below.

Q: Evaluate L{t² cos t}

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

Q: f(x) = a cos(bx) а cos

A: Given,                         f(x)=acos(bx)+cx+dif a=6, b=0.5, c=3 and d=4.

Q: /2 cos a sin(sin r) dx

A: using method of substitution

Q: tan y = In 2 + e"

A: Given : tany = ln2x2+e-xy

Q: Rewrite sin(x + ¹(x + 11T) 6 sin (z + 11T) = in terms of sine and cosx.

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Q: Prove that d/dx [cos x] = −sin x.

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Q: Verify the identity: (sec t - 1)/t sec t = (1 - cos t)/t

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Q: If f(x) f' (æ) = 2 sin x + 11 cos x, then f'(2) = %3D

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Q: Sketch X,(t) and Xa(t) Where X,() = - Sim3t Sin3t %3D 3. X,(e) = /a Sin 3t %3D

A: To draw the graph of functions X1(t)=-13sin3t and X2(t)=13sin3t, substitute different values of t in…

Q: Differentiate  cos t sin t

A: We have to differentiate cos t sin t. Given function is: f(t) = cos t sin t Then we get,  ft=122 sin…

Q: Differentiate (sin(ax+b)/cos(cx+d))

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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