Prove the following identities and show complete solution 1 + sin 2B + cos 2B cotß %3D 1+ sin 2ß – cos 2B

Q: Find the product of zı and z2 Given zı = 4 (cos 180 ° + i sin 180 °) and Z2 = 4 (cos 145° + i sin…

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Q: 2 v sec 2 1+ cos 0°

A: We have to find the identity

Q: sec(θ)=11/3

A: Please refer to the image below

Q: Find all solutions to 2 cos(0) = 1 on the interval 0 <0 < 27 %3D

A: Given : 2cosθ = 1

Q: Prove the following identity: sin(21) 1+ cos(2x) tan(z) 1

A:

Q: ) Prove that 2+sinZA Cos A-SinA

A: To Prove: cos3A-sin3AcosA-sinA=2+sin2A2

Q: 4. Express the following in cartesian form. 2 2 cos 03 sin

A: Given r=22cosθ-3sinθTo express in cartesian form:

Q: Prove the following identities: sin 6+ sec 0) +(cos 0+ sece) = (1+sec0 cosece)

A: We can easily prove this given identity shown below

Q: Value of L is 16 $3+9s 16 O(1 + sin 31) 16 O (1 + cos 3t) 16 (1+ cos 3t) 3 (1 - cos 3t)

A:

Q: Prove that: 2n 1 cos=0 + i sin 0) + 10 2cosne - %3D eino

A: If  is an exponential form of a complex number where x and y are real numbers then its polar form…

Q: prove the identity  sin^4(t) - cos^4(t) = 2sin^2(t) - 1

A: We know that ,  sin 2 ( t ) + cos 2 ( t ) = 1  cos2 ( t ) = 1 - sin 2 ( t )

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: Prove the following identity: 1+ cos(2y) sin(2y) 1+ cos(2y) sin(2y) 1 tan(y)

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Q: Find the product of z1 = 2 (cos 213° + i sin 213 °) and Z2 = 4 (cos 33 ° + i sin 33 °) %3D

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Q: Find 0, if 0° <0 < 360° and 1 and 0 in III. 2 cos 0 =

A:

Q: Prove using the IVT. tan-1x = cos-1x has a solution.

A: Given :                      tan-1 x = cos-1 xSolve :                     tan-1 x = cos-1 x…

Q: Q2/Prove that cos 17° + sin17° = tan62° cos17° – sin17°

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

Q: Prove the following: sin² 0 – cos² 0 = 1– 2cos² 0 %3D

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Q: 10. Prove that (지12 sin 8 cos 1 (cos a cosec 0) de 1/2-a (1-cos a )

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Q: Evaluate the integral | : sin 20 do 3+ cos 20 using the substitution u = 3+ cos 20. sin 20 Op 3+ cos…

A: In this question, we need to evaluate the integral ∫sin 2?3+cos 2?d? using the substitution…

Q: 10. Prove that 7/2 sin 0 cos (cos a cosec 0) do -(1-cos a). 2 ||

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Q: Express the following as a product of factors (1) sin 2x+sin6x +sin 8x (11) cos 54+ 2cos3.4+cos.4

A: We know that sin C + sin D = 2 sinC+D2 cosC-D2 cos C + cos D = 2 cosC+D2 cosC-D2

Q: Evaluate the integral : sin 60 do 2+ cos 60 using the substitution u = 2+ cos 60. sin 60 do = +C 2+…

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Q: The suitable substitution to evaluate sin24(x+2) dx is None 1 [1- cos4 (r+2)] [1+ cos8(r + 2)]…

A: Topic- integration

Q: Give the exact value of COS (-) + sin ( 3 V3 O1 2 2 O V2 O 1+v3

A: We need to find the exact value of the given trigonometric ratios.

Q: Compute cos (cos-1(3/2)) O 3/2 O This quantity does not exist.

A:

Q: Prove the below cos' x sin 3x + sin' x cos 3x 3 sin 4x 4 II

A: Simplification of trigonometry function

Q: 27. Evaluate: cos 2) - sin 6 4 /3 /2 2 2 1 V2 V3 2 2 1 V2 2 None of the above. + |

A: Hence option (c) is correct.

Q: Show that 2 cos(x) = 3x has exactly one real solution.

A: As we know that if the function is strictly increasing, f'(x)&gt;0 or strictly decreasing,…

Q: Evaluate the integral: 3 X sin ³ COS 3 3 X col 3

A: Solved below.

Q: 5- Prove the following (Answer two only): secA. secB.cscA.cscB a- cos*e – sin*o =cos²0 – sin²e c- =…

A: Answer 2 only.

Q: 57 then If 0 = sin(0) = %3D cos(0) = %3D

A: Given θ=5π6

Q: Evaluate the integral / sin 50 do 2+ cos 50 using the substitution u = 2+ cos 50. sin 50 do 2+ cos…

A: Recall: ∫1xdx=ln(x)+C

Q: 3 Verify the identity: csc (0) 1-cos2 (0) cos (20) 2 sin(0) + 2tan(0) cos(0) = %3D sin (0)

A:

Q: 4. Express in the form a + jb, (i) 2(cos 30° +j sin 30°) (ii) 5(cos 57° -j sin 57°)

A: To write in the form of a+jb

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: 1. By considering (1+ expi®)", prove that "C, cos r0 = 2" cos"(0/2) cos(n /2) (ii) ►"C, sin r® = 2"…

A: First, expand the given complex function:

Q: Use the addition formula to prove                                                             cos 3θ…

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Q: Q2\ Prove the following identities sin 20+cos 20+1 a) = cote sin 20-cos 20+1

A: Here given equation   sin 2θ+cos 2θ+1sin 2θ-cos 2θ+1=cot θ

Q: Prove the following identity 1+ cos(2y) sin(2y) 1 tan(y) 1+ cos(2y) sin(2y) %| %3D

A: Solve the following

Q: Find z where z = sin (æ²) cos (4²) COS

A: The given function is z=sinx2 cosy2.

Q: Find all values of 0, 0° < 0 < 360°, that satisfy 5 cos 20 + 7 sin 0+1 = 0

A: 5cos2x+7sinx+1=0REwriting we get:6-10sin2x+7sinx=0sinx=-12, sinx=65Combine all the…

Q: Prove the following identities and show complete solution 1 Cos 8x - sin²2x + cos²2x %3D 8.

A: The relation between the angles of a triangle and the sides of the triangle can be defined with the…

Q: Prove that; (a) cos4θ- sin4θ = cos 2θ  (b) Sin (π/4 + A) + Sin (π/4 - A) ≡ √2 cos A

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Q: Prove by MSE that a. sin 90° = 1 b. cos 180° = -1

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Q: Show that 4 sin x cos 2x + 3 = 8 cos %3D x.

A: We will use the formula of cos 2x and other formulas of trigonometry to prove left hand side is…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.