Find an expression that is mathematically equivalent to (1 - cos(x) / 2) and in which excessive cancellation cannot occur, that is, in which numbers that can be almost equal are not subtracted.

Q: 3 dx \8+7 cos x

A: Given: ∫38+7 cosxdx

Q: By expressing the product as a sum, 2cos(3x)cos(4x)= ?

A:

Q: s if 0 < x <277 -cos 2xsin x

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Q: One of the values of x from the equation 2 csc(x) = 4 over the interval [0, 2π) is 5.

A:

Q: 4). Evoluate 2. (88e0 COS X cot x)dx 4

A: Definite integration

Q: Suppose S (x) =sin(3x – 2). Evaluate: /f(x) dr A - 3cos(3x – 2) + C (A) (B ® --cos(3r – 2) + C ©…

A: Given, f(x) = sin3x-2To evaluate:∫f(x) dx This can be done as follows:

Q: 6.5 Show that for all x. sin x = m = 0 (-1)m x ²m+1 (2m + 1)! and COS X = m = 0 2m (-1)"x2" (2m)!

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Q: If csc e = 1/3t, then where defined, cos 0 A) Square root of (1 – 9t²) 3t/squareroot of (1 – 9t2)…

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Q: Solve the following equation forz: √8- cos (22) = 3. 0x==²(1) Co OI= cos ¹ (1)-2 Oz=(-1) Ozcos¹ (2)…

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Q: ; Choose the most appropriate answer. (i) Let 1-r 2 E (an cos(ntx) + bn sin(nrx)], n=1 on (-1,1).…

A: This is Fourier series expansion of (1-x) from -1 to 1.

Q: n/2 1+2cos x Q:Evaluate: dx. (2+cos x)*

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Q: Solve 424 sin2 x-1 1 for x e (0,).

A: Note:

Q: √√3 tan-¹x 4. (10 points) Evaluate SY 1+x2 dx (using substitution).

A: The value of the integral is 7 pi^2 / 288.

Q: Evaluate the following * S sin(4x) dx O cos(4x)/4+C -4cos(4x) + C O-cos(4x)/4 + C O-4cos(4x) + C

A: We can find the answer as below.

Q: Q10: csc (x + 360) = cos x * True O False

A:

Q: Find d. dr /1 + x²

A: We have to find the derivative and then anti derivative.

Q: dx Evaluate: /9 – x² A @ sin -1 +C .3. 1 3 sin +C 3. B

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Q: Prove that 2+1> (n + 2) · sin(n) for all positive integers n.

A: Concept: Principle of mathematical induction: For each natural number n, mathematical induction is a…

Q: In/cosh(2x)– sinh (2x)): Select one: O 2x None O O

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Q: @ Suppose that f(n) = corn, g(n)= e. Using numerical affronimation find I (0-8), 9²(0) for the…

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