Prove the Product-to-Sum Identity sin A cos B = (1/2)[sin(A+B)+sin(A-B)] Start with the right-hand side: (1/2)[sin(A+B)+sin(A-B)] = %3D = (1/2)[(sinA)( B) + ( %3D A)( B) + (sinA)( B) - ( A)( B)] = %3D =(1/2)[2( A)( B) + 0] =sin COS -hand The last expression is the side of the original equation, hence, the proof is complete.

Q: Express cos- (a) in terms of cos(2a). Express sin (a) in terms of cos(2a).

A: This question is of double angled identity.

Q: Find (f-1)'(a). f(x) = 3x³ + 2 sin x + 3 cos x, a = 3 (f-1)'(a) = Need Help? Read It

A: Given:- f(x) =3x3+2 sin(x) +3cos(x)  To find:- (f-1)'(a)

Q: Prove the identity. 3 sin(x - y) 3 tan x - 3 tan y = cos y cos x

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Q: 1. What is the exact value of sin 75°? O -V6-V2 4 O vô-v2 4 O v2-V6 4 O V2+v6 4

A: We have to find the value

Q: sin(26) cos(26) – 1 1 Prove the following identity: - tan(b) sin(26) cos(26) – 1

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Q: 4. a. Find the exact value for: tan(5) b. Solve for x: tan(2x) = √3, x€ [₁] 2

A: (a) The objective is to find the exact value for tan5π3. (b) Given equation tan(2x)=3,  x∈-π2,π. The…

Q: 1. Explain why sin(n+0) =-sin@ using a diagram and x, y, and r.

A: Solution of given problem is followed by

Q: (ii) Prove the identity (2 - 2 cos 0)(sin 0 + sin 20 + sin 30) -(cos 40 - 1) sin 0 + sin 40 (cos 0 –…

A: Prove the Identity: 2-2cosθsinθ+sin2θ+sin3θ=-cos4θ-1sinθ+sin4θcosθ-1 NOTE: Since you have asked…

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Q: sin(1+ cos(0)) Find lim 1+ cos(0) Select one: О a. -1 O b. 1 Oc-2 O d. 2

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Q: Using an appropriate identity, compute the exact value of sin(375°). V3-V2 4 V6-V2 2 V2+v3 4 O v2-1…

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Q: sin 0 If 1+cos 0 x2 x2, then tan 2 - a) b) 4 c) x2 + 1 d) x2 |3| 2.

A: Given,  sin θ1+cos θ=x2 To determine tanθ2

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

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

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Q: sin e 1 cos 0 Multiply - by 1 + cos 0 1 - cos 0

A: According to the difference of squares formula, (a+b)(a-b)=a2-b2. Using the difference of squares…

Q: sin (1) Using an appropriate substitution, evaluate: [2+ cos(1) ]* 1 +C A 3[2+ cos(1)]³ 3 B +C [2+…

A: topic - Indefinite integration

Q: a. Apply the formula for cos (A – B) to the identity sin 0 = - 0) to obtain the addition formula for…

A: a) cosA-B=cosAcosB+sinAsinBPut, A=π2, B=θThen,  cosπ2-θ=cosπ2cosθ+sinπ2sinθ…

Q: Prove the identity step by step.  cos4 x-sin4 x=cos2x

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Q: Evaluate (cos x In sin x) dx. Select the correct response: O cos x (In sin x-1) +C sin x (In cos…

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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: 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: sin ( 27 +1)x Prove that dx =7 for all ne N. Sin x

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Q: 1. Determine (i) |cos (2x– 7) dx dx (ii) x +9 (ii) dx 4-9x² 2. Determine (sin x cos x dx using (1)…

A: Since, you have posted multiple questions we will only first question with three subparts as per our…

Q: 16) Complete the identity. sin^2 x-1=

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Q: The identity sin1 x  cos1 x  P,2 Figure 1.69 establishes the identity for 0 6 x 6 1. To…

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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: Evaluate / (cos x)~ª (csc x)-³ dx. Select one: 1 O a. csc³ x – sin x + C а. O b. None of these 1 O…

A: Given integral to evaluate ∫cosx-4csc x-3dx=∫1cos4xcsc3xdx…

Q: 1) prove the identity tan(A)sin(A) = sec(A) − cos(A)

A: We will use trigonometrical identity to find solution to the problem . According to bartleby…

Q: 2 sin 50 do. 9. Use the residues' theorem to evaluate sin o

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Q: 1 cos 0 Prove the identity = tan 0. coc A 1tcin A

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Q: sin(cos (0.5354)) = O 0.8446 O 1.8446 O -0.1554 O -1.1554 O 2.8446

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

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Q: sin(cos(0.3866)) O -1.0778 O 2.9222

A: We have to solve the problem

Q: 4. Establish the identity using the sum and difference formulas: sin (m – 0) = sin 0

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Q: (cos^4 x) - (sin^4 x) = cos2x   verify the identity

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Q: 5. Prove the identity. csc 0- cot 0 sin- 2 2 csc e

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Q: cos e sin 0 for some real value of 0, and let B= -1 Let A = Consider x - sin 0 cos 0 Then ||(AB)x||…

A: Given,            A=cosθsinθ-sinθcosθ , B=0-1-10 , x=12To find : ABx

Q: Prove the identity. sin x 1+ cos x 1- cos x sin x

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Q: sin 0(3sin? 0+ 4cos? 0) = 3 cos 0 + cos³ 0 4. Prove that tan 0

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Q: a. Apply the formula for cos (A - B) to the identity sin x = cos(pai/ 2 - x) to obtain the addition…

A: a). Obtain the addition formula for sin(A+B) using the identity as follows.

Q: Find cos a if tan a= (√2)/2 and sin a=-(√3)/3

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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: 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: CoS X Which of these is an efficient first step in proving the identity 1+ sin x 1- sin x :? cos X

A: To prove cos x1+sin x=1-sin xcos x

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Q: Verify the identity. sin (e + n) = -sin e A) sin (e+x) = cos Osin e- cosa sin a = cos Osin e--0 =…

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Q: 7. Prove the identity. – sin 3 TT -x= 0 2 sin +x 2

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Q: Let sin A = 4/5 with A in QII and sin B = − 8/17 with B in QIII. Find sin(A + B), cos(A + B), and…

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