Prove each of the following identities.     sin 3 theta = 3 sin theta - 4 sin 3 theta

Q: Find the exact value of each of the following under the given conditions below. 3 3n sin a =. -7<a <…

A:

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: Use Euler's identity to (a) show the identities (i) cos(@ + B) =cos(a) cos(B) –- sin(a) sin(B), (ii)…

A: Hey, since there are multiple question posted, we will answer the first question. If you want any…

Q: Prove each of the following trigonometric identities. 1 + tano : 1+ sin& coso coso

A:

Q: 2. Write each of the following numbers in the form of a + bi a) cos(3 – i) b) 2i sin h (4 – ni)

A: The given expressions are: a) cos3-i b) 2isinh4-πi Write each of the following numbers in the form…

Q: Prove that each of the following statements is not an identity by finding a counterexample.   sin…

A: The given equation is sinθ+cosθ=1   Known fact: sinπ6=12cosπ6=32

Q: Prove each of the following identities.     cos  3 theta  = 4 cos 3 theta  - 3 cos theta

A: To prove cos  3 theta  = 4 cos 3 theta  - 3 cos theta

Q: Prove the following identities.         sin theta tan theta + cos theta = sec theta

A: We have to prove: sinθtanθ+cosθ=secθ We know following relations for trigonometric ratios:…

Q: Prove each of the following identities.     cot theta - tan theta = cos 2 theta / sin theta cos…

A: Given: prove that cotθ-tanθ=cos2θsinθcosθ for solving this we simplify left hand side we know that…

Q: Show that each of the following statements is true by transforming the left side of each oneinto the…

A: Given that: The statement sin θtan θ = cosec θ .

Q: Evaluate each of the following: 1. [ sin 5.x sin xdr

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Verify the following identity: 2. sin y - 1 1 sin y -1 sin y

A:

Q: Prove that each of the following identities is true.   cos x / 1+ sin x  + 1+ sin x  / cos x  = 2…

A:

Q: Show that each of the following statements is true by transforming the left side of each oneinto the…

A: Given that; The equation sec θ - cos θ = sin2θcos θ  .

Q: Which of the following statements must be true? Select all that apply. sin A = cos A sin B = cos A

A: Explanation and solution is given below....

Q: Prove each of the following identities.     cot  theta  = sin 2 theta  / 1- cos 2 theta

A:

Q: Prove that each of the following identities is true.     tan theta cosec theta cos theta = 1

A:

Q: Prove each of the following identities.     sin 4 A  = 4 sin  A cos 3 A - 4 sin 3 A cos A

A: Given: prove that sin4A=4sinAcos3A-4sin3AcosA for verifying this we solve left hand side using given…

Q: 3. Verify each of the following identities. b. csc(20) = sec 0 csc 0 CSC

A:

Q: Prove that each of the following identities is true.   tan theta  - cot theta = sin 2  theta - cos 2…

A: To prove: tan θ-cot θ=sin2θ-cos2θsin θ cos θ

Q: Prove that each of the following identities is true.   sec theta  - cosec theta = sin   theta - cos…

A: Given identity is: secθ-cosecθ=sinθ-cosθsinθcosθ Since, sinθ and cosecθ are reciprocal to each…

Q: Show that each of the following statements is true by transforming the left side of each oneinto the…

A: we have to show that the following statement is true . 1-cosθsecθ=sin2θ

Q: Show that each of the following statements is true by transforming the left side of each oneinto the…

A:

Q: Prove that each of the following identities is true.   1 + sin theta  = cos 2 theta  / 1- sin theta

A: To prove 1+ sinθ =cos2θ1-sinθ

Q: Prove each of the following identities.     2 cot 2 x=  cot x - tan x

A:

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

A: Given: cosx-π2=sin x To show: The given identity is true.

Q: Prove each of the following identities.     cosec theta - 2 sin theta = cos  2 theta /sin theta

A: To prove : cscθ-2sinθ=cos2θsinθ.

Q: Prove each of the following identities.     sin 2 theta  = 1- cos 2 theta /2

A:

Q: Write each of the following in terms of sin theta only .   cos theta

A: we have to write each of the following in terms of sinθ only cosθ

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

A: Explanation: There is a Trigonometry Identities that: cos(A−B)=cos(A)cos(B)+sin(A)sin(B)

Q: Prove each of the following identities.     cos 2 theta  = 1+ cos 2 theta /2

A: To prove the identity,  cos2θ=1+cos2θ2 Consider the right side of the identity and show that is…

Q: Prove the following Sin? Z + CoS² z = 1

A: To prove that sin^2z+cos^2z=1

Q: Prove the following identities.         ( 1+ sin theta ) ( 1 - sin theta  ) = cos 2 theta

A: To Prove: 1-sin θ1+sin θ=cos2 θ Consider Left Hand Side- 1-sin θ1+sin θ= 11+sin θ-sin θ1+sin θ=1+sin…

Q: tan (0+180°) =tan(0).

A: We need to prove the identity:tanθ+180°=tanθ.We will use the formula:tanx+y=tanx+tany1-tanx. tany…

Q: 2. Prove each of the following identities: (a) tan x sin x + cos x = sec x Answer:

A: tan x sin x+cos x=sec x

Q: Prove that each of the following identities is true.   cos x / 1+ sin x  + 1- sin x  / cos x  = 0

A: Given : cos x / 1+ sin x  + 1- sin x  / cos x  = 0   Taking LHS, = cos x / 1+ sin x  + 1- sin x  /…

Q: Prove that each of the following identities is true.   cosec 4  theta  - cot 4 theta  = 1+ cos  2…

A: To prove: cosec4θ-cot4θ=1+cos2θsin2θ

Q: Show that each of the following statements is true by transforming the left side of each oneinto the…

A:

Q: Prove that each of the following identities is true.     sin 4 A -  cos 4 A = 1- 2 cos 2 A

A: In order to prove the identity sin4A-cos4A=1-2cos2A, start from the left hand side and prove the…

Q: Find the exact value of each of the following under the sin a = 13' 2/13 0<a<z cos ß= COS 13 2B<0…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: Find the exact value of each of the following under the given conditions. 7 2/29 0 < a<5; cos ß = 25…

A:

Q: Prove the following identity: cos(60) 1– 18 sin? 0 + 48 sin4 0 – 32 sin® 0 =

A:

Q: Prove the following identity. sec2 A 2 sec A %D sec A + 1

A:

Q: Prove that the following identity is true. sin? x(cot? x + 1) = 1

A: Given : sin2xcot2x+1 = 1

Q: Show that each of the following statements is true by transforming the left side of each oneinto the…

A: To prove : cosθcosecθtanθ=1 Formula used : Trigonometric identities : tanθ=sinθcosθcosecθ=1sinθ

Q: Prove that each of the following identities is true.     cosec theta  tan theta = sec theta

A: cosecθ*tanθ=secθ