a) Use the formulas  sin(A + B) and sin(A - B) for toshow that sin A cos B = 1/2 [sin(A - B)+ sin(A + B)](b) Use part (a) to evaluate  ∫sin 3x cos x dx.

Q: Use the method of substitution to evaluate | 2x cos x² dx. sin x? + c – sin x? + c sin x? + c sin x-

A: We use substitution method

Q: a) cosx = - ja 0 <x< 360° b) sin (2x +) = 0, ja - << c) 2cos?x + sin +x) – 1 = 0, ja 0 <x<2=

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Q: Match the trigonometric expression cos2[(π/2) − x] /cos x with its simplified form. (a) csc x (b) −1…

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Q: Show that A" cos (ах ah + b) = | 2 sin cos a + bx +n (ah + T 2

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Q: 1-cos . Fill in the blank: sin(_) = V 2 O 7y

A: As per our guidelines we are only supposed to solve first question in case of multiple questions

Q: Find all values of x in the interval [0, 2?] that satisfy the equation. 6 cos(x) + 3 sin(2x) = 0

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Q: 1- Determine. 4. Cos 'x sinX dx

A: Given:                     ∫cos4(x) sin(x) dx     Solution:                    Integrating the given…

Q: 3- Represent in the form of x+ iy a) V8 (cos + i sin m) b) 6 (cos 7 + i sin7)

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Q: Rewrite cos ( x in terms of sin(x) and cos(x) 3 -

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Q: Using the substitution u = sin (x), or otherwise, find the exact value of %3D J sin° (x) cos (x) dx.…

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Q: Express the 10th term of ( x1 + x2)º in terms of sinusoidal functions (sin, cos).

A: The expression is x1+x220. As we have obtained…

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3 C=/2 A 18 cos²0d0 (B) 1852/200…

A: See the details solution in below

Q: What is (cos x + x) dx? O-½ sin²x + x²/2 + C ○ -sin x + x²/2 + C O sin x + x²/2 + C O. ½ sin²x +…

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Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: Given: 4∫sinx cosx dx=-cos2x+C To Determine: Whether the statement is true or false. If it is false,…

Q: Use the appropriate formula to express the product sin x cos 2x as a sum or difference.

A: Given Data The product of trignometry formula is sin x cos 2x.   The general formula for the product…

Q: Find sin 5, given that sin x = 2 i and 0<x<5.

A: Here  sin x=14⇒cos x=1-sin2x              ⇒cos x=1-116              ⇒cos x=154 Now, sin2x2=1- cos x2…

Q: (a) Prove that Sin-1x  + Cos-1 x  = π/2 .(b) Use part (a) to prove Formula 6.

A: a) We have to prove sin-1x+cos-1x=π2 Let sin-1x=θ                                     ⋯⋯1…

Q: Find the exact length of r = 3 sin 0 + 4 cos 0. II

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

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Q: 3. Using the fact that sin 2a = 2 sin a cos a, and the fact that 0 = 2a, rewrite the area of the…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Rewrite cos x+ in terms of sin(x) and cos(z). 4

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Q: Another form of sec x dx cos x 1- sin²x b. Use the identity in part (a) to verify that 1. |1 + sin…

A: a) we have to verify the identity sec(x)=cos(x)1-sin2(x)Consider, RHS=cos(x)1-sin2(x)we…

Q: Complete the statements.

A: Given Our aim is to complete the sentence

Q: Given that sin-(x) = a and cos-(x) = B show that sin(a + B) = 1. %3D

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Q: Verify the identity. cos 2x cos² r - sin? x

A: We have to solve the trigonometry problem

Q: Which is equal to (sin⁡x+cos⁡x)^2+(sin⁡x−cos⁡x)^2 using identities?

A: Now we use identity  Sin2x +cos2x =1 And formula (a+b)2= a2 +b2 + 2ab  (a-b)2 = a2 + b2 - 2ab

Q: Sec A - cos A is identically equal to

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Q: 1 200 -1 1 What is the value of the -coordinate of point A?

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Q: Determine COs x-2 = 0. correct to four decimal places, a root OF the equation sin X+3 %3D

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Q: 2. Plot sin (x) and cos (x) on the same figure, then on the same axis using different colors. Where…

A: The graph of sinx for 0&lt;x&lt;2π is:   The graph of cosx for 0&lt;x&lt;2π is:

Q: What is the period of f(x) = sin(3Ħx – 4) + 2? %3D

A: For a given function: Time period (T) =        2(PI)     _        w(omega) Whereas addition of DC…

Q: Find a numerical approximation to the length of c(t) = (cos(4t), sin(8 Use decimal notation. Give…

A: Given

Q: Rewrite cos ( x in terms of sin(æ) and cos(x). 4 -

A: we know that cos(a-b)=cosa cosb+sina sinb

Q: rewrite cos(x+4pi/3) in terms of sin(x) and cos(x)

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Q: Can the Intermediate Value Theorem be used to prove that the equation 9 2(r + 9) sin*(x) – 4 cos"(x)…

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Q: Evaluate 2 sin x cos x dx by three methods: (a) Let appearance of the answers obtained in (a), (b),…

A: To evaluate: I=∫2 sin x cos x dx

Q: Show that sin x – cos x< V2 V2 -

A: Take RHS first and work on that:

Q: sin (x) = 0.8. If x and y are complementary, what is cos (y)?

A: In the question it is asked to calculate the value of cos(y) for sin(x)=0.8. It is given that x and…

Q: To evaluate sin e de , factor sin³e as (sin²e) ² sin® and let sin²0 =-(1- cos20). A True B False

A:

Q: Using a suitable substitution, (sin x cos“ x) dx can be 4 (A) - f u*du (B)

A: Given: ∫0π2sinxcos4xdx

Q: Is this: sin x cos y- cos x sin y/ cos x sin y reciprocal quotient pythagoreom  algebra

A:

Q: Prove that cos(sin-x) = /I– x².

A: Given: sin-1x=cos-11-x2

Q: 2. Given that csc A = v2, A in QI, and sec B V5, sin B <0, find: a. cos (A- B) b. tan (A- B) %3D

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: How would you evaluate∫cos2 x sin3 x dx?

A: Given: ∫cos2xsin3xdx

Q: Determine whether the following statement is true or false. If y = sin¹ (4x4), then = 16x³sin³ (4x4)…

A:

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: **/2 Ⓒ 18/¹/2 (A) sin²0d0 0 **/2…

A: See the details solution in below

Q: Prove: sin? xcos?x = - cos(4x). 8.

A: We will use various trigonometric formulas to prove the given identity.

Q: The expression 4tan(x)sin(x)+2sec(x) simplifies to A sec(x) − B cos(x), determine A and B. A= B=

A: The given expression: 4tan(x)sin(x)+2sec(x)

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.