Derive the Formula for sin(A – B) [Hint: Use the formula for sin(A + B) and properties of even and odd functions]

Q: Find all values of x such that sin 2x = sin x and 0 <x< 2m.

A: sin 2x=sinx⇒sin 2x-sin x=0⇒2 sin x cos x -sin x=0⇒sin x2 cos x-1=0⇒sin x=0  or  2 cos x-1=0 sin…

Q: Is sin-1 x the same thing as1/sin x?

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Q: 2. What is the exact value of tan (-75°)? O 2-V3 O-2+ V3 O 2+ v3 O-2-V3

A: To find :  The exact value of tan(-75°). Note: To find the exact value apply the reference angle by…

Q: 7. What is the exact value of tan (-105°)? O -2 – V3 O 2 - V3 O 2+ v3 O -2+ V3

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Q: True or False sin² 0 = 1 – cos² 0.

A: Use the trigonometric identity sin2θ+cos2θ=1 to verify the statement.

Q: Establish the identity. sin =1- sin x

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Q: Write an algebraic formula for sin[(sin^-1(u)-cos^-1 (v)]

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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: Rewrite sin(x+ 7) in terms of sin a and cos I. Enclose arguments of functions in parentheses. For…

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Q: Find an alternative form in terms of x for each of cos(sin- 1 x) and tan(sin- 1 x).

A: Let us make a triangle with opposite = x and hypotenuse=1 , because sin theta= opposite/hypotenuse…

Q: Show there exists exactly one solution to the equation 3x = 2 cos x + 1. %3D Explain your reasoning,…

A: Answer is given below

Q: A. Find the exact value of the composite function. sin sin 4

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Q: Find a value of x that satisfies the equation sin 13° cos (x). %3D

A: We know that Sin(x)=Cos(90-x). so...Sin(13)=Cos(90-13).

Q: Prove the identity: (sin x – cos x)(sin x + cos x) = 2 sin² x – 1

A: As value of cosθ and sinθ revolves around +1 to -1 , they take different values depending on the…

Q: Show that the functions f and g are identically equal.

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Q: Find the real zeros of each trigonometric function on the interval 0 ≤ θ&lt;2 π. f(x)= cos(2x)+sin2…

A: f(x)=cos(2x)+sin2(x) for finding the zeros we put f(x)=0 sin2(x)+cos(2x)=0we know cos2x =…

Q: Rewrite 1 sin(x)+ 2 cos(x) as A sin(x + 4) %3D Note: o should be in the interval-T <¢ < II

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

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Q: B- find the value of x x = tan(sin-1–) 2.

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Q: Complete the statements.

A: Given Our aim is to complete the sentence

Q: (b) Explain that function f(x) = 1 is not perpendicular to sin(x) or to sin(3x), but is…

A: Introduction: The inner product space is a map from the Cartesian product of vectors space V×V to…

Q: Can i get help step by step?

A: Given

Q: tan e 2. Find the domain of the function f:0→. 2 sin e-3 cos e

A: Domain for any function fθ is defined as the real values for θ for which fθ exists. The given…

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

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Q: 3元 What is the exact value of sin ? Show your work. 2

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Q: 1) Prove that cos°(x) + sin (x) = 1. (refer to notes). Use the "Square" formula.

A: See the attachment

Q: prove the identity  sin(x) + sin(3x) = 4 sin(x) cos2(x)

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Q: Determine the domain and the range of the function f(x) = sin-1 x + cos-1 x

A: To determine domain and range of the given function.

Q: )-tan (-V3) 4. Find the exact value of expression sin cos -1 /2 2

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Q: Prove that sin x+ cos -1 -1

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Q: [cos 0 -sin 01, Verify A. AT = I ii. Let A= sin 0

A: We verify that A.A^T = I

Q: a value of x that satisfies the equation sin 53° = cos (x %3D

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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 all values of x in the interval [0, 2π] that satisfy the equation.  sin x = tan x

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Q: B- find the value of x x = tan(sin-1) 2

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Q: Express the function below as a sum or difference of sine and cosine.    sin 4x cos 3x

A: Given: y=sin4xcos3x We know that 2sinAcosB=sinA+B+sinA-B                                         ..1

Q: what is the derivate of sin(x)cos(x)?

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Q: 24. Prove the identity 1 – (sin x – cos x)2 = sin 2x

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Q: Identify the trigonometric function from the graph. 2 a) f(x) = 2sinx b)f(x) = 2+ sinx c) f(x) = 2+…

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Q: What is the period of G(x) = 5 sin(3x - 3pi)? 2pi 2pi/3 2pi/5

A: Finding the period of G(x)

Q: Is f(x)=cos^2(x)-sin^2(x) even, odd, both, or neither?

A: Given,           f(x)=cos2(x)-sin2(x)

Q: Complete the statements.

A: a). As x→-1+, sin-1x→-π2

Q: Verify the identity: cos4 t - sin4 t = 1 - 2 sin2 t

A: We have the identity cos4t-sin4t=1-2sin2t   Consider LHS LHS=cos4t-sin4t Rewrite as…

Q: Evaluate and show your work a. sin (π - x) + cos (3π/2 - x) b. sec3π/4csc5π/4 + tan4π/3cot11π/6…

A: To Evaluate: a. sin (π - x) + cos (3π/2 - x) b. sec3π/4csc5π/4 + tan4π/3cot11π/6 c. Tan-1(-√3)

Q: Verify: cos? x tan? x- 1 1. -1 cos2 x

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Q: /2 Find the exact value of sin sin 2.

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Q: 19.Solve the trigonometric equation:                        Tan x sin x  - tan x = 0    [ 0 , 2π)

A: The value of the tan function is 0 at θ=0, π in the interval [0, 2π). The value of the sine function…

Q: Derive the formula for Sin(A-B) (Hint: use formula Sin(A+B) and even/odd functions

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Q: Evaluate: cos x-sin(sin x)dx and explain your answer in terms of odd/even functions.

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Q: Determine if the statement is true or false.    2 sin  A/ 2 = sin A

A: Given : 2 sin  A/ 2 = sin A   Taking LHS : = (2 sin  A)/ 2 = sin A