(c) Prove that cos 35°+cos 45°+cos 75°+cos 85° = 2 cos 5° cos 20°.

Q: Graph the function. 10) y - 2 + cot x 10)

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Rewrite the expression as a sum or difference a) sin52.5° sin97.5° b)prove the identity…

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

Q: b) sin 1 с) cos 2x - 2

A:

Q: 7. (a) Write 1 + 2° + 33 + 43 + 5° using sigma notation. (b) Write 2k² without using sigma notation.…

A: A series can be represented in a compact form, called summation           or…

Q: Given z₁ = 8(cos 45° + i sin 45°) and 2₂ = 4(cos 210° + i sin 210°), what is 2₁2²2?

A:

Q: 3) Use a sum/difference formula to solve: Evaluate sin (a – B) if sin a = (a in first quadrant), and…

A: We have, sinα = 45, α is in first quadrant cosβ = -1213, β is in second quadrant To evaluate : The…

Q: 14. If Cos 2 A.Cos 2B = Cos 20, prove that: Sin² A.Cos² B+Cos² A.Sin² B = Sin²0

A: Given We have to prove .

Q: 3. Show that cos 30 = cos 0 – 3 cos 0. [Hint: Apply De Moivre's Theorem.] |

A: Given: verify that cos3θ=cos3θ-3cosθ according to given hint theorem cosx+isinxn=cosnx+isinnx

Q: Using De Moivre's theorem, show that in 40 2 cos 0. = 8 cos³ 0-4 cos = 2 cos 30 +

A:

Q: If sin (A – B) = 1/2, cos (A + B) = 1/2, and 0° B, then A =

A: Given : sin(A-B)=12  and cos (A+B)=12sin(A-B)=12 ⇒ A-B=sin-112A-B= 30°…

Q: O) sinßcosa + cosßsina sin 60°cos 45° + Cos (G0°sin 45°

A:

Q: Use the factor formula to prove that sin 5° + cos 35° = sin 65°.

A: Explanation of the answer is as follows

Q: 2) If Sin A= 3/5 Then Find the value of Cos 2A O 24/25 O ((24)/25 7/25 O (-7)/25

A: Given: sinA=35cos2A=?

Q: Find the 3rd roots of 27 (cos 45° + i sin 45°) a. 3 (cos 15° + i sin 15°) C. 3 (cos 135° + i sin…

A:

Q: What is 7(cos (pi/2) + i sin (pi/2)) divided by 8 (cos (3pi/4) + i sin (3pi/4)) equal to?

A:

Q: . Given that t d s T and cos d = Delermine each. 13 -) sind ) cos2d

A:

Q: 6. Prove the given identity (clearly show ALL your steps): 1+cos(2A) cot?(A) 1-cos(2A)

A: We have to simplify

Q: Use de Moivre's formula to derive the trigonometric identity cos 30 = cos³ 0-3 cos sin²0.

A: We need to prove the identity: cos3θ=cos3θ-3cosθsin2θ. cosθ+isinθn=cosnθ+isinnθ for n∈ℤ   We know…

Q: Prove that cos0cos20cos40..... cos2″ 0 = sin2n+¹0 22+¹ sine

A:

Q: 8) Solve each equation on the interval 0 < 0 < 2n. a. 2 cos² 0 + cos 0 – 1 = 0 b. 2 sin? 0 – 5 sin 0…

A: Solve the equation on the interval 0≤θ≤2π a) 2cos2θ+cosθ-1=0…

Q: 5 3n 3 b) Given sec A = 4 for the interval 2 <A< 2n and cot B = 2 for the interval 2 <B<n, evaluate…

A:

Q: & tan B give

A: We have to find