If sin(0) >0 and cos(0) = - find tan(0). CO %3D tan(0) =

Q: COS (+3 O cos x Ocos 2x O sin a Ocos z +x) + cos (-) is equivalent to:

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Q: If sin' 0+y cos e sin e cos e and x sin e = y cos 6, prove that x + y* = 1.

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Q: Suppose that 1 a + sin x ) dx = 15x 1 + x2 -1 What is the value of a Your answer should be an…

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Q: -y = tanh" (cos e* ) ||

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Q: 2.1 Given that sinh x = [e" – e=*] - - show that dy cosh a. da

A: To Determine: show that dydx=cosh x Given: we have sinhx=12ex-e-x Explanation: we have…

Q: Find the solution of the equation = e Cos y which tends to zero as x → 0o and has the value cos y…

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Q: Recall that cos- arccos x. Find r1/2 e sin(cosx) dx. 0.

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Q: The approximation of I = = co cos (x²+5) dx using simple Simpson's rule is:

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Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B} sin²x + C {C}-{cos²x + C {D} sin 2x + C

A: A detailed solution is given below

Q: a) y = sin x² cos 2x 4.

A: Given: y=sinx2cos2x, y=cos4sec23x We know that ddxuv=vdudx+udvdx…

Q: I Eliminate the arbitrary constants -2x 2X Y = C,e cos 2× + Ge sin 3X

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Q: If k0 then the trigonometric integral [ 3 sin³ (kx) dx is equal to [−sin(kx) + sin³(kx)] + C the…

A: To evaluate the integral.

Q: 6. Suppose you wish to differentiate g(x) = sin²(x)+cos²(x). What is the fastest way to do this, and…

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Q: coS x dx 6) 1 + 3 sin x A) In| 1+3 sin x|+C C - 를 In| 1 +3 sin x| +C

A: To evaluate ∫cosx1+3sinxdx

Q: 4. Evalaute cos(x) sin(x) dx

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Q: Show that L{cos at} = S s² + a² Hence find L{sin 8t sin 6t}.

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Q: Suppose A is the annihilator of y= e*sin(x) – 3cosh(x), if f(x) = A(sin(x)), determine the value of…

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Q: Find the smallest positive solution of cos x = eX; x0 = 1 by iteration.

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Q: 3- If a y + sin y + arctan a = sin 1 then what is the value of at (0,1)? dz -2 b)- 1+ cos 1 -1 1 a)…

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Q: (a) / sin sin(8x) + cos(7.x) dx (b) / (3x – 5 sin dx 2 (c) / cos(3t) + sin(5t) dt

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Q: (a) Show that cos(x²) > cos x for 0 ;. 1

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Q: sinh(Inx)dx 1) 2) fe* sinade e*.sinxdx 3) sin? (2x).cos(3x) G

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Q: a. Solve for real x, in the equation sinh 2x – 2 cosh 2x + 2 = 0. b. Express tanh x in terms of e*…

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Q: Compute S cos (x) sin²(x) dx

A: To solve the given integration problem ∫cos3(x).sin2(x) dx

Q: S cos ( x^3 ) dx = * sin ( x^3) + c 3x^2 sin (x^3 ) + c - sin (x^3 ) + c - 3x^2 sin ( x^3) + c none…

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Q: find sin x cos? x dx 75. 76. sin 2x sin (cos 2x) dx er dx et + e* (e2x + e)² dx 77. 78. x + 1 e* + 1…

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Q: (1 + cos 7t) 2 sin 7t dt

A: Here we use u-subsitution to evaluate the integral. d(cosx)dx= -sinx

Q: y = e2* (c, cosx+ c, sin x)

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Q: Given In = S cos" x dx = - cos"-1 x sin x + In-2 ; %3D n/2 determine a reduction formula for cos" x…

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Q: 5. The function f(0) = (sin O+cos 0) + (sin 0– cos 0) may be written as

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Q: b. Express tanh x in terms of e* and e-* and hence show that 2 tanh x tanh 2x = 1+ tanh? x' c. Given…

A: (b) To proof :   tanh2x=2tanhx1+tanh2x It is known that, sinhx=ex-e-x2coshx=ex+e-x2 so,…

Q: Find the solution of the equation = e cos y which tends to zero as x→ 00 and has the value cos y…

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Q: 9. cos (2t) dt 10. " sin?t cost dt /2 11. sin'x cos?x dx 12. (2 sin0)² d®

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Q: Find the solution of the equation cos y which tends to zero as x- 0o and has the value cos y when x…

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Q: 6. S sin*(e³*) cos(e³*) e³× dx

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Q: Suppose x and y are functions of a third variable t. If sin-(x) + cos°(y) = = and dr dy what is the…

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Q: 3. S sin? (2t) cos³ (2t) dt 4. ſ tan³(3x)dx

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Q: 11. sin(x) + cos(y) = ey

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Q: 18. S sin xdx 2-cos² X

A: The given integral is: I=∫sinx2-cos2xdx    ...1 As we know the common integral; ∫11-x2dx=sin-1x+C

Q: S 4 cos (x) sin (x) dx = %3D

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Q: 4. S(1 – cos 4u) du 5. S sin x cos x dx

A: 4) Given:        ∫1-cos4udu Apply linearity:    =∫1 du-∫cos4u du     =u-∫cos4u du

Q: Find cos (0 + p) given that cos 0 = 2 and cos p = 2 and that 0 and p are between 0 and t/2.

A: For the given values of  Cos(θ)=1213 Cos (ϕ) = 35 Cos(θ+ϕ ) is evaluated as shown below

Q: Find the exact value. 3 S sin cos 2 0 x dx

A: Follow the procedure given below.

Q: integrate cos^2(t)*sin^2(t) from 0 to 1

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Q: The result of solving the integral x' tan(x²) dx is: A) Inlcos(x) +c B) tan(x)-+ In/cos(x²)|+c D) +1

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Q: 2 Recall thal cos-x= arccos x, Find /2 X Sin (cos x) dx. C.

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Q: cos x 6) dx is equal to sin x A. In/2 В. Inv3 C. In" D. In e

A: The  given integral is ∫π4π2cosxsinxdx

Q: Suppose x and y are functions of a third variable t If sin2(x) + cos²(y) =- and dr dy what is the…

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