103. Prove that for all whole numbers n > 1, sin x = sin (x + d" dx" Hint: Use the identity cos x = sin (x +).

Q: 8. Evaluate the integral. sin x xp. 4+ cos x

A:

Q: If f(x)= cos (x)+3x , what is f'(x) ? COS O f'(x)=-sin (x) +3

A: First option is correct. Explanation is given below....

Q: 41. Show that if u = tanh(x/2), then 2u 1+u? 1- u?' 2du 1- u? cosh x = sinh x = 1- u? dx = Hint: For…

A: To show the following

Q: (-n *) Prove sin? x – sinx cosx – 2 cos? x =0 in п, 2 has five root's Hint. Intermediate value…

A:

Q: Q5. If coshx = csc20, prove that 0 = n+ cothe¯. [Hint: use identity sin(2a + 2n)] %3D

A: given that                                                                             coshx=csc2θ…

Q: Q3) Ify = in[sec 8 + tan 8) find

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Q: Prove the following inequalities (ii) -10|< sin 0 < |0| and -|0| < 1– cos 0 < |0|

A:

Q: 5) Evaluate the integral: tan 3 x dx

A: Given integral, ∫tan3x dx

Q: 6. Prove the following sin (x + n) = -sin x cos x+ 2 - sin x

A: Part a,Given,           sinx+π=-sinx

Q: Show that sin mx cos nx dx = 0 for positive integers m and n: i using the primitive, ii using…

A:

Q: Evaluate the indefinite integral sin (2)cos"(2)dz 4

A:

Q: Verify the following results  sin 4x = 8 cos3 x sin x − 4 cos x sin x

A: Given questions are two individual questions. So as per bartleby expert policy only one individual…

Q: 2. Extend the identity cos(ax)-cos?x-sin'x for xE PR to the identity cas (a2)- Cos s 2-sinz for & €…

A:

Q: Evaluate the indefinite integral.  ∫sin(3x)cos(6x)dx=________________ +C

A:

Q: 4) state laylors your estima te 5) Using in Taylor's Theorem, show that the error in 3) for cos…

A:

Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

A:

Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

A:

Q: Prove the following identities. Set up using LS/RS a. cos(² + x) = sin x b. sin(2x) 1-cos(2x) = cotx

A: a) The given identities: cos3π2+x=sinx To prove the given identities.

Q: Evaluate the integral | : sin 20 do 3+ cos 20 using the substitution u = 3+ cos 20. sin 20 Op 3+ cos…

A: In this question, we need to evaluate the integral ∫sin 2?3+cos 2?d? using the substitution…

Q: 4. Use the inequality | sin r|< |x| for x E R to show that the sine function is continuous at r = 0.…

A: Sine function and it's continuity at 0

Q: Evaluate using Wallis' Formula: So sin® x cos4 x dx -Tt/2

A:

Q: Use the Intermediate Value Theorem to prove that sin x − cos x = 3x has a solution, and use Rolle’s…

A:

Q: 3. Give upper and lower estimates (in terms of n alone) for sin nb COs na + valid for all a, b; show…

A:

Q: 77. Evaluate f sin x cos x dx using substitution in two different ways: first using u = sin x and…

A:

Q: If 1, = | x" sin x dx, prove that 1, = nx"-! evaluate -1,. sin x- x" cosx– n(n-1)I, 2. Hence, = NX…

A:

Q: Find all values of x in the interval [0, 27] that satisfy the equation sin x sin x tan x

A:

Q: 11.. , Evaluate each definite integral. a) cos² x sin x dx

A: Use substitutions to integrate

Q: 25. Assuming that (d/dx) (sin x) = cos x and (d/dx) (cos x) = - sin x, prove each of the following.…

A: Our Aim is to prove the derivative of the following:-(i) ddxtan (x)=sec2 (x)Proof⇒ddxsin (x)cos…

Q: 1. Determine the absolute extrema of f(x) = (sin x – 1) cos x on 2' 2 if they exist, and identify…

A: Given:-f(x)=sinx-1cosx,        x∈-π2, π2f'(x)=sinx-1ddxcosx+cosxddxsinx-1…

Q: Evaluate the following integral. 8 sin x sin 2x dx fean: |8 sinx sin 2x dx =|

A:

Q: (b) Can we use the IVT to conclude that f (x) = tan(x) equals 0 for some c in (0, 1)? %3D

A: We can answer first question among which you asked as per the honor policy. please resubmit the…

Q: 278. Suppose that sin(ln x) = 3, and that sin(ln y) = }. If 0 < ln x < and 0 < ln y < , use the…

A:

Q: evaluate the definite integral.

A:

Q: Evaluate the integral / sin 50 do 2+ cos 50 using the substitution u = 2+ cos 50. sin 50 do 2+ cos…

A: Recall: ∫1xdx=ln(x)+C

Q: Evaluate the definite integral 15 sin (3x) cos(3x) dx

A:

Q: Use the addition formulas to deriv TT 31. cos(x - sin x 2

A: Prove that cos( x  - π/2 ) = sinx Here we use general formula : cos( A - B ) = cosA×cosB + sinA×…

Q: Evaluate the indefinite integral. cos x dx (sin x)27

A: Let's find.

Q: Evaluate integral 0 to pie sin 2 x cos 4 x dx

A: To Evaluate the integral given below:-I=∫0πsin2(x)cos4(x)dx

Q: Let I = S sin 2xdx be given. After substituting y = tan x, how can 5 cos? x+7 sin? x the integral I…

A: Given :

Q: 17) Prove the following: a) (sin x)(sec x)(cot x) 1

A: Since secx=1cosx  and cotx=cosxsinx Then LHS =  sinxsecxcotx=sinx1cosxcosxsinx

Q: /2 Evaluate using Wallis' Formula: sin5 x cos6 x dx

A:

Q: Q4: Prove that: cos?x – sin?x = 1- tan?x cos?x

A:

Q: Which of the following is equivalent to [sin(-x) + cos(-x)]? 1 - 2sinxcosx O 1 O 1+ 2sinxcosx O…

A: Use Trigonometric identities and simplify.

Q: -Tt/2 Evaluate using Wallis' Formula: 7 sin5 x cos6 x dx

A:

Q: 5. Integrate the following and show all of your work: sin“ r cos r dr

A: we have to integrate the following

Q: Q2/ Evaluate the following: sin 2x+cos2x+1 1- Prove- cot x sin 2x-cos 2x+1

A:

Q: 52. Verify that f(x) sin x is an odd function and u fact to show that '3 sin x dx < 1 -2

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Q: csch(3 tan x) + sin² x cos² x dx

A:

Q: (6) Given that In= tan" x dx, show that, for n 2 2. %3D In- In-2 = %3D n- 1

A: I think given question is slightly wrong. According to me the required proof should be…