In Exercises 45-48, graph each side of the equation in the same viewing rectangle. If the graphs appear to coincide, verify that the equation is an identity. If the graphs do not appear to coincide, find a value of x for which both sides are defined but not equal. 45. sin x + sin 2r = sin 3x 46. cos x + cos 2r = cos 3x 47. sin x + sin 3x = 2 sin 2x cos x 48. cos x + cos 3x = 2 cos 2x cos x

Q: Use addition formulas and the values of sin θ and cos θ for θ = π/3 , π/4 to compute sin π /12 and…

A: To calculate sin π /12 sinπ12=sinπ3-π4=sinπ3cosπ4-cosπ3sinπ4=32·12-12·12sinπ12=3-122

Q: Verify that the equation is an identity. 2 sin x tan 2.r = 2 cos x - sec x

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Q: Find sin x/2, cos x/2, and tan x/2 from the given information. csc x = 8,   90° < x < 180

A: Given cscx=8 ,where 90°&lt;x&lt;180°. Here, x lies in 2nd quadrant, so sinx will be positive but…

Q: 9. What is Sin(210 deg)= %3D always check if the answer should be positive or negative. *

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Q: Find the exact value of cos2 15° - sin2 15°.

A: We have to find the exact value of cos2 15°-sin2 15°Formula used :-Cos 2θ= cos2 θ-sin2θ -1

Q: Evaluate the exact value of 4 /5 tan sec 4

A: The objective is to evaluate the exact value.

Q: Find sin 2x, cos 2x, and tan 2x if sin x - and x terminates in quadrant II- sin 2x %3D cos 2x %3D…

A: Use the fact that in second quadrant cos and tan are negative.

Q: In Exercises 45–46, express each sum or difference as a product. If possible, find this product's…

A: 45. sin2x - sin4x

Q: Verify the identity.

A: We have  cosx-5π2=sinx   It is known that cosA-B=cosAcosB+sinAsinB   Consider LHS:…

Q: 79. Sin x = 2 +an 즐 14 tan'즉

A: Prove the identity Take RHS

Q: = Cosx (2

A: Using identity sin(a+b)=sin(a)cos(b)+cos(a)sin(b), we will verify the given identity

Q: Find the exact value of sin 5π/12 using the fact that 5π/12 = π/6 + π/4.

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Q: Give all solutions of the equation sin2x cos x= cos x in the interval [0°, 360°)

A: Given equation is By using the identity we get

Q: what is the value of x if cos(5x+10)°=sin(4x−1)

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Q: Find sin 2x, cos 2x, and tan 2x if tanx=-3 and x terminates in quadrant II.

A: Giventanx=-3 and x is in II quadrantWe have to find sin 2x , cos 2x and tan 2xTo find sin 2x use…

Q: In Exercises 43–48, find the exact value of each expression. Do not use a calculator. tan 3 1 43.…

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Q: Find sin 2x, cos 2.x, and tan 2x if cosx 2 and x terminates in quadrant II.

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Q: 2. What is the exact value of cos()? |(0, 1) (글,

A: Graph is symmetrical in -2 to 2. So the midline of function is y=0.

Q: Rewrite as a single quotient and simplify. sin 0 + cos 0 cos 0 – sin 0 - Cos 8 sin 0

A: We need to rewrite as a single quotient and simplify.

Q: A = -, find sin 2. If 90° <0 < 180° and cos 0 :

A:

Q: Use an identity to solve the equation sin 3x cos 2x + cos 3x sin 2x = 1 on the interval [0, 2π).

A: From the given data:

Q: For Exercises 37-40, verify that the equation is an identity. (See Example 4) 37. sin(-x) + cscx =…

A: To verify:sin(-x)+cscx=cotxcosx Solution: Considering, LHS sin(-x)+cscx On simplifying further we…

Q: For Exercises 51-56, verify the identity. 20 _ csc 0 - cot 0 sec 0 + 1 51. sin? 2 52. cos? 2 53.…

A: To prove -  sin2θ2 = cscθ - cotθ2cscθ

Q: Given that sin2   x + cos2  x = 1 and sin x = −√2/5, what is the possible value of cos x

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Q: Part 3 of 4 COS X d —CSC X + С dx To check for the result, prove that 1 - cos?x

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Q: Use a calculator to solve the equation 3 cos2 x - 8 cos x - 3 = 0, correct to four decimal places,…

A: We have the given equation as, 3cos2x-8cosx-3=0 On solving further, we get the result as…

Q: Find sin 2x, cos 2x, and tan 2x from the given information. 4 COS X = 5' * csc x < 0 sin 2x = cos 2x…

A: We answer the questions as below.

Q: Show that the equation sin(cos 2x)= V1-4x² is an identity. %3D

A:

Q: 4 sin“ x = 1 – 2 cos 2.x + cos² 2.x

A: 4sin4x=(2sin2x)2 Using cosine double angle formula which is cos 2x=1-2sin2x1-cos 2x=2sin2x…

Q: If the terminal side of a contains the point (-12, –5) and the terminal side of B.contains the point…

A:

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. cos(x) =  12 13,   csc(x) < 0…

A: We shall use the trigonometry identities   Sin2x +cos2x =1 Sin2x= 2sinx Cosx   Cos2x= 1- 2sin2x…

Q: Graph each side of the equation cos 1.2x cos 0.8x - sin 1.2x sin 0.8x = cos 2x in the same viewing…

A: cos1.2x cos0.8x-sin1.2x sin0.8x=cos2x The graph is,

Q: sin 60⁰ cos 300⁰

A:

Q: Use an identity to solve the equation: cos x - sin x = -1, 0 ≤ x &lt;2π.

A: Given: cosx-sinx=-1; 0≤x≤2π for finding solution of given equation, we simplify it so,…

Q: 4. Find the exact value of sin if cose 2 3 and e is in QIII. cose =-- |

A: According to question,Given conditions,cos θ = -35,θ is in third quadrant.

Q: Suppose that sin 0 = and 5 %3D - Find the exact values of cos and tan - 3.

A:

Q: 3. Prove the identity by transforming the left side of the equation to match the right side. Do not…

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Q: ㅠ ㅠ Solve the problem. Usesin = = landsin = 4 ㅠ Use the formula sin(2x) = 2 sin x cos x, with x = 4…

A: We can find the answer as below.

Q: Find cos if sin = 1/2 terminates in QII

A: Given data:     The given value of the trigonometric identity is: sinθ=1/2.     Evaluate the given…

Q: Determine whether the statement "Although sin-1 (-1/2) is negative, cos-1 (-1/2) is positive." makes…

A: Using the ASTC rule, we know that sine is positive in the 1st and 2nd quadrant. But since sine…

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

A: Given : cos(x - 23π) To find : Rewrite the given function in terms of sin(x) and cos(x)?

Q: 37 in terms of sin(x) and cos(x). Rewrite cos 4

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Q: Verify the identity: tan θ = (1 - cos 2θ)/sin 2θ..

A: Given, tanθ=1-cos2θsin2θ

Q: Verify that the equation is an identity. 2 cos x 1. cos X 1. 1+cos x 2.

A: It is trigonometric verification.

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. cos(x) = 12/13 ,   csc(x) < 0

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