Prove that : n/2 1 dx (a'sin'x + b’cos'x 4a°b³

Q: Evaluate sin (44º) + cos (29º) using differentials. Refer to special triangles.

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Q: Evaluate the integral. |cos 7x cos 3x dx

A: The given integral ∫cos7xcos3xdx.

Q: Integrate: So a sin(x²) dx

A: We have to integrate

Q: Evaluate the integral f sin²(3x) cos (3x) dx.

A: The given integral is ∫sin23xcos53xdx. We have to evaluate the given integral.

Q: Prove that  d/dx[cosx]=-sinx

A: We will use the definition of the derivative  Here f(x)=cos(x) So,

Q: Find dy/dx  if  4 cosx siny = 1

A: We will directly differentiate it.

Q: Evaluate the integral.  integral sin 9  x cos 3x dx

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Q: Find integral.

A: We have to find the integral I=∫cos(5x) dx

Q: If y- sinhx then prove that = dx

A: Fundamental inverse Trigonometric Identities: →cosh2y - sinh2y = 1 Basic derivative:…

Q: x sin 2x sin cos x 2 Prove that: dx = 2x- T

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Q: If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx

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Q: If cos(0) 1 and 0 satisfies T < 0 < , find sin(0). 2 - sin(0) = %3D

A: Given: cos θ=-16 &amp; π&lt; θ&lt;3π2 To determine: sin θ

Q: [ cos² 2x sin² 2x dx

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Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

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Q: Prove that 2 arcsin (x) = arccos (1-2x2) for XE (0, )

A: arccos1-2x2 Put x=sinθ, we get arccos1-2x2=arccos1-2sin2θ=arccoscos2θ      ∵cos2x=1-2sin2x=2θ=2…

Q: Show that x² + 1 cos{arctan[sin(arccot x)]} = V x² + 2

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Q: d Prove that sin x cos x from first %3D dx principles only. Be sure to prove any limits that are…

A: Let's learn first principle of derivative because we have to find derivative of sinx using first…

Q: Find the indefinite integral. ∫sin7 2x cos 2x dx

A: Consider the given integral ∫sin72xcos2xdx

Q: E prove that - Cotx + C %3D 2 |- Cos?x +Sinx

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Q: E prove that = - Cotx + C %3D 1- Cosx +Sin'x

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Q: )if x+tany+ sin-x+ In(yx) +3**1 =4 then find y'

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Q: (b) Show that 2t cos x and sin x = 1 + ? (c) Show that dt dx 1 +

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Q: 3 4. sin x cos xdx

A: These formulae are used while solving the question:

Q: Consider sin¹x cos³x dx. If we let u= sinx, the integrand can be transformed to

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Q: Evaluate the integral.  integral sin 9  x cos 5x dx

A: Given :           ∫ sin9 xcos5 xdx

Q: sin x + 10(csc x)² dx

A: To compute: ∫(sin x+10(csc x)2)dx

Q: Use Simpson's rule with n = 6 to approximate cos(x) rp-

A:

Q: Compute the indefinite integral. ∫(1−sin2x)/(cosx) * dx

A: The given integral is,

Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: Find the definite integral of ƒ™/* cos 3x sin 5x dx. -π/4 Option 1: Option 2: Option 3: Option 4:…

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Q: The integral O cose de 1-sine sec²0 de 1+ tan sece tane de sece - 1 S sine de 1+ cose x dx can be…

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Q: 35. Use property IV of Appendix A to verify that 1 L'{arctan(a/s)} =sin at

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Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: cos (6x) cos (3x)dx

A: Solution :∫cos6xcos3xdxNote…

Q: f(x) = cos (In (3x))

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Q: Prove that: sinhx + coshx = e* %3D

A: we have  sinh(x)=ex-e-x2cosh(x)=ex+e-x2

Q: 4. Ify =/sin x+ /sin x+.to inf inity, dy _ cosx dx 2y-1 prove that

A: Derivative of Sinx is Cosx

Q: x sin 2x sin COSX 8. Prove that: %3D 2x-7

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Q: S cos (2x) sin* (2x)dx a.

A: Solution: The objective is to evaluate the integral

Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

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Q: sinx f(x) = on [0, 2n] cos x-V2

A: Given :         f(x) = sin xcos x - 2 on 0, 2π   To determine the extrema of the above function…

Q: Prove that 55 sin x² dx - 5 cos x² dx = 1/2 √

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Q: Show that cos(arcsinx) Vi - x², for x| s lin two different ways.

A: Show that cosarcsin(x)=1-x2, for x≤1

Q: e). Prove that Sin3A+sinA 25in2A -COSA

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Q: The approximation of 1 = f*cos(x³ - dx using composite Simpson's rule with n= 3 is:

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Q: Evaluate the integral cos3 x + sin² x + 1 dx cos² x (sin2 x + 1)

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Q: Evaluate integral 0 to pie sin 2 x cos 3 x dx

A: Explanation: Given that,  ∫0πsin2xcos3xdx   Formula Used: Trig. identity:1-sin2x=cos2xSum rule of…