Expand and simplify the following sin(x+3π/2)+cos(x+3π/2)

Q: establish the following identities: sin3x=(sinx)(4cos^2 x-1)

A: Given,

Q: Express each of the following products as a sum or difference: a. sin 8x sin 3x   b. sin 4x cos x.

A: Given: a. sin 8x sin 3x b. sin 4x cos x.

Q: Find the identical expression for the following. cos x 1+ sin x 1+sin x cos x 2sec x O 2csc x 2cscx…

A: To solve the following trigonometric identity.

Q: Prove the following identity sin−1 x = cos−1(1 − 2x2)          x ≥ 0.

A:

Q: PROVE that sin x = V1 – cos² x is NOT an identity. -

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Q: Say whether the following statements is true or false sin2t.dt 2-1(1 ~-²¹ (5(5²2 + 4) ==—=— 'sin2 +4…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: Show that each of the following is true.     sin ( 3 pi/2 - x) = - cos x

A: Given: prove that sin3π2-x=-cosx we know that sinA-B=sinAcosB-cosAsinB

Q: Prove the following identities. cos( - ) sin x/2

A: NOTE: Refresh your page if you can't see any equations. .

Q: Verify the following identity. 2 sin x+ cos 2x = 1- sin x

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Q: Differentiate the following expression: y=x² cos 4x

A:

Q: Analyze the following identities. a) cos¹0 - sin¹0 = cos 20 COS b) (sin x + cos x)² = 1 + sin 2x

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Q: valuate the following in the form of a + bi : (cos 30 + i sin 30 ) 4 (A) -0.5 + 0.866i B 4 cos 30 +…

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Q: Compute the following: sin² (x) dx

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Q: The following are solutions of sin2x+sinx=0 EXCEPT А. 3. B.n D. 3 O A O D

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Q: Find the values of x in 4 cos2 x = 1

A:

Q: Evaluate the following Rational Fractions -(3 cos² 0 + 8 cose-12) sine de cos³ 0+7cos² 0+ 12 cos 0…

A: The given integral is;  -(3cos2(theta) +8cos(theta)-12)sin(theta)/(cos3(theta)+7cos2(theta)…

Q: Which of the following is equal to cos x- sin' x ? 4 | O sin 2x O - sin 2x | O - cos 2x

A:

Q: Express the following as a product of factors (1) sin 2x+sin6x +sin 8x (11) cos 54+ 2cos3.4+cos.4

A: We know that sin C + sin D = 2 sinC+D2 cosC-D2 cos C + cos D = 2 cosC+D2 cosC-D2

Q: Evaluate the integral ∫1/θ2 sin 1/θ cos 1/θ dθ

A: Given- ∫1θ2sin1θcos1θ dθ To find- The value of the integral. Concept Used-  The above integral can…

Q: -20 sinh(2a) 2 O True O False

A: We need to tell if the statement is true or false. this can be done as follows:

Q: Evaluate or simplify the given expression. sin(2 tan -1 3x) 3x O 9x2+1 6x O 9x² + 1 3x O 9x2 + 1 6x

A:

Q: Prove the following identities and give the val- ues of x for which they are true. cos 12 sin-lx2 =…

A: cos2sin-1x Now let, sin-1x=θ Therefore, cos2sin-1x=cos2θ=1-2sin2θ      ∵cos2x=1-2sin2x=1-2x2…

Q: Prove each of the following identities.     2 sin4 x + 2 sin2 x cos2 x = 1 - cos 2x

A: Given, 2sin4x+2sin2xcos2x=1-cos(2x)

Q: (4) |sin² 0 cos0 d0

A:

Q: Express the following product as a sum. 2 cos(9x) sin(3x)

A: We have to express the product as a sum: 2 cos9x sin3x We know the identities: sinA+B=sinA cosB+cosA…

Q: Express each of the following products as a sum or difference: a. sin 5x sin 2x   b. cos 7x cos x.

A: We have to express as a sum or difference for the products: a. sin 5x sin 2xb. cos 7x cos x We know…

Q: Find an equivalent expression to sin (z+) a) sin(2)-√3 cos(z) 2 b) √3 cos(z)+sin(z) 2 O c) -…

A:

Q: 4. Verify the following identities: a. sin 3x = 3 sin x-4 sin3 x b. 1+ cos 10x = 2 cos? 5x %3D

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Q: Prove the following identities. sin 2x csc x =

A: Topic:- trigonometry

Q: Evaluate the following: 1.) sin*3x cos 3xdx

A: To evaluate the below integral. ∫sin43xcos33xdx

Q: Which one of the following is not equal to cos 4x for all real values of x? A sin? 2x – cos? 2x B 2…

A: Follow 2nd step.

Q: Let sin A = 3/5 with A   cos  2 A

A: Given Sin A=35Formula for compound angle Cos2A=1-2Sin2ATo computeCos2A…

Q: Verify the following identities: a. sin 3x = 3 sin x-4 sin x b. 1+ cos 10x = 2 cos 5x %3D

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Q: Use an addition or subtraction formula to find the exact value in simplest form. Rationalize your…

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Q: Integrate each of the following without using trigonometric substitutions. _cos(x) xp- J sin(x) + 3

A: Integration is a way of adding pieces to find the whole.

Q: Write a formula for cos 2x by writing cos 2x as cos (x + x) and using the formula for the cosine of…

A: cos2x

Q: Give the exact value of 37 sin(- 00 O undefined 1 O V2 2 2 V3 O-1

A: Here I am attaching image so that you understand each and every step.

Q: Graph each of the following from x = 0 to x = 2pi  y = sin 5x cos 3x - cos 5x sin 3x

A: Given that: y=sin5xcos3x-cos5xsin3x,    0≤x≤2π

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: Derive the following formulas: cos 2x =1-2 sin² x

A:

Q: Evaluate the following 2 sin (x) 1+ cos (x)

A: We know that, sinx=2sinx2cosx2          ⋯⋯1cos2x=2cos2x2-1               ⋯⋯2 We have the given…

Q: Prove each of the following identities.  (sin x 2 cos x)2 =1 - sin 2x

A: To prove:           (sin x  - cos x)2 = 1 - sin 2x

Q: Evaluate the following integral: * *π/2 [sin² 6 1/42 4 O - (2/63) O - (3/28) O 2/63 sin x cos³ x

A: The objective of the question is evaluate the definite integral and choose the correct option.

Q: Evaluate the following 2 sin (x) -dx 1+ cos (x)

A: I = ∫0π/2sin(x)1+cos(x)dxI = ?

Q: 4) Evaluate the following 2 sin (x) 1+ cos (x)

A: Evaluate: ∫0π2sinx1+cosxdx