Show that cos bx = (eibx +e-ibx) and 1 sin bx :(eibx – e-ibx). 2i (A comparison of these formulas with the correspond- ing formulas cosh bx =(ebx 1 +e-bx) and sinh bx =(ebx - e-bx) indicates why the trigonometric and hyperbolic func- tions satisfy similar identities.)

Q: in−1(x) + cos−1(x) =  ? 2

A: Given that : The equation is sin-1 (x) + cos-1 (x) = π2 .

Q: If cos 4x = cos 6y, which of the following is correct?

A:

Q: Cos x = Cos" x 1-

A: In this question we have to prove cosx=cos-1x.

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: Given that the sin x = 2/5 and cos x = -1/4 with sin x in Q1 and cos x in Q3, find sin( sin x - cos…

A:

Q: Find sin 2x, cos 2x, and tan 2x if tanx= and x terminates in guadrant III. 3

A: To find the value of sin (2 x), cos (2 x), and tan (2 x).

Q: 3 with A e QIII , find sin2A 8 7. If cos A =--

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

Q: Find sin(2x), cos(2x), and tan(2x) from the given information sec(x) = 4, x in Quadrant IV %3D…

A: Given: secx=4, x in Quadrant IV   We know that; The trigonometric identities; 1). sin2x+cos2x=1 2).…

Q: To evaluate the integral sin ³0cos (A) sin²0=1-cos²0 1-cos20 B sin ²0 2 sin20 sin cose 2 1+ cos20…

A:

Q: 4 Suppose that sin e -and <0<1. Find the exact values of cos 2 and tan 2. Cos 2. = D tan, 2) %3D

A: As we know sin2θ+cos2θ=1. cosθ=1-452=1-1625=-35 Using Double angle formula: sinθ2=1-cosθ2=1+352=810…

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = - x in Quadrant II| 3'…

A:

Q: The integral ¹S. 01-fese csc ³0 de sin² sin ²0 de = [sec³ sec ³0 de + cos² cos²0 de dx (x²+4)² can…

A: We have to solve Integral

Q: 1 Prove that sec 03D Cos 0

A: Let P(x,y) be a point on a circle of radius r associated with the angle θ.

Q: 1. Use the Intermediate Value Theorem to show that there is the solution to the equation cos(x)=x in…

A: Given cosx=x

Q: Find sin2x, cos2x, and tan 2x if cosx - and x terminates in guadrant III. 13 sin 2x cos 2x tan 2x

A:

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: Find sin - and cos 2' given that cos 0 and 0<0 < 3

A: Please refer the attached image for complete solution. THANK YOU.

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

A:

Q: Use the Intermediate Value Theorem to prove that sin x − cos x = 3x has a solution, and use Rolle’s…

A:

Q: By using the relationship between the hyperbolic sine function and its inverse, prove * (sinh (z)] =…

A:

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. sec(x) = 8, x in Quadrant IV sin(2x)…

A:

Q: Given that sin-(x) = a and cos-(x) = B show that sin(a + B) = 1. %3D

A:

Q: Find the exact value of cos(α − β) if α and β both lie in the first quadrant, and sin α = 12/13 and…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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

A:

Q: 15 Suppose that tan a = TC <a<t. 2 and - Find the exact values of cos and tan 2 - JT Cos Undefined…

A:

Q: 8 and x terminates in guadrant IV. 15 Find sin 2x, cos 2x, and tan 2x if tanx %3D

A: Given  tanx=-815,  x in quadrant IV

Q: Evaluating ³√9-x² dx using trigonometric substitution will lead to: 15/2 A cos²0d0 B 18 cos²0d0…

A:

Q: - If z = (1 + cos + i sin -)°, find the cubic roots of z in the sin 2. 2- Exponential form.

A:

Q: 3. What is (Sin (6x)}? 4. What is (Cos (x²) dv 5. What is (tan x³) dx 6. What is (In x)7

A: we use the chain rule to find the derivative of the given function

Q: 12 Find sin 2x, cos 2x, and tan 2x if sin x=- and x terminates in quadrant IV. 13 sin 2x %3D cos 2x…

A:

Q: 1 tan z = 3'

A: The value of tanz =13  is given where, π≤z≤3π2 Solution: (a) Now  we have ,tanz =13, So -tanz will…

Q: To evaluate sin 2x cos 2xdx conveniently, the formula/ identity to be used islare A sin²2x =1– cos2x…

A: We need to choose correct option.

Q: if cos A=1/2 with A in QIV find sec A/2

A: Given  We know that

Q: Prove that, cos20 + sin?0 = 1

A: Let a, b and c be the lengths of right angled triangle. Then by definition,

Q: Find (a) sin 2t, (b) cos 2t and tan 2t given the following: 1) cost = −5/13 , and π/2 0 3) tant =…

A: The detailed solution is given below Thank you

Q: To evaluate sin42x cos 2x dx , the identities to be used is/are: A cos?2x=1– sin2x 1+ cos4x & 2…

A:

Q: Let sin A = 3/5 with A   cos  2 A

A: Given Sin A=35Formula for compound angle Cos2A=1-2Sin2ATo computeCos2A…

Q: Use DeMoivre’s Theorem to find z4 if z = 2 (cos 3π/4 + i sin 3π/4). Write your answer in standard…

A:

Q: Q3-Prove that (cos30=cos³ 0-3cos 0 sin? 0)

A: Using compound angle formula &amp; trigonometric identities.

Q: 11.Show that A cos (ω0t) + B sin (ω0t) can be written in the form r sin(ω0t − θ). Determine r and θ…

A:

Q: If tan θ= √2/5 and π (less than) θ (less than) 3 π/2, find the exact value of cos 2 θ

A: Given tanθ=25   If π&lt;θ&lt;3π2 then  cos2θ=?

Q: Find the value of cos-1(2) using Euler's formula.

A: We find cos-1(2) , by using Euler's formula.

Q: To evaluate sin 2x cos 2xdx conveniently, the formula/ identity to be used islare A None 1- cos4x…

A:

Q: Prove: sin? xcos?x = - cos(4x). 8.

A: We will use various trigonometric formulas to prove the given identity.

Q: To evaluate | sin42x cos 2xdx conveniently, the formula/identity to be used islare A sin²2x=1–…

A:

Q: 33. Use addition formulas and the values of sin 0 and cos 0 for 0 = to compute sin 12 and cos…

A: Given: sin7π12, cos7π12 We know that sinA+B=sinAcosB+cosAsinB…

Q: To evaluate the integral 1 sin20 A sin cose= 2 1-cos20 B sin²0= 2 1 + cos20 (c) cos²0=- 2…

A: In this question, we want to know which identify is useful to solve the Integral.

Q: To evaluate sin 2x cos 2x dx , the identities to be used is/are: sin4x , 1+ cos4x A 2 2 ® cos?2x=1-…

A: To find The identities to be used.